My reply was, ask me again at the end of September. We're 10 days away from that mark and I can give you my answer now.
No they can't.
While one reserves the right to be pleasantly surprised and have the above served up with humble pie, the last three league games have shown that a serious improvement is needed for this to happen.
The 3-1 defeat to Aberdeen at Tynecastle showed that as far as challenging for the big prize goes, there is a gap that needs to be closed.
That could well happen but many at Hearts need to step up if they are serious about fulfilling such a lofty aim.
At Inverness, they looked half-asleep while today, the players looked like they had just met each other for the very first time.
When up against a cohesive unit like Aberdeen, the ill-advised fragmented approach will crumble every time.
The basic errors were unacceptable and got their just desserts from an Aberdeen team that is genuinely challenging for the title.
Callum Paterson is one case in point and some would feel that this particular performance from him was coming.
The right-back plays, what is known as, a 'tightrope' style of game. He's not afraid to take plenty of risks and when they come off, the rewards have been good for Hearts.
But like the boxer who likes to take a dicey chance of dancing around the ring, he does so in the knowledge that one slip can lead to him being knocked out.
One masterful exponent of this was the legendary Sugar Ray Leonard. However, instead of playing football in the same manner in which Leonard would approach a bout in the ring, Paterson today was Kirkland Laing instead.
Many fingers will point to goalkeeper Neil Alexander for Aberdeen's first goal.
They would be right to do so as this was a 'bread and butter' save that should have been made from David Goodwillie's header instead of squirming through Alexander's olive-oil coated gloves and into the net.
However, that incident came about because of an equally silly error from Paterson seconds earlier.
Chasing a ball punted down his flank, Paterson, with Goodwillie breathing down his neck, had time to hoof it into the stands and, at worst, give away a throw-in.
Instead he tries to shield the ball out for a Hearts throw when every man and his dog can see that the ball is not going to run out of play.
Goodwillie sees this as well and gets in behind Paterson to retrieve it. The latter panics and fouls the former to concede a free-kick from which Aberdeen score.
His error for Aberdeen's second was even more glaring.
Having skinned a leaden-footed Blazej Augustyn, Aberdeen's Niall McGinn bore in on goal from the left. Paterson was the last barrier before Alexander but instead of standing his ground, he tried to be clever and second-guess McGinn thinking he would be pulling the ball back for a Don's team-mate to shoot on goal.
Only he forgot the golden of rule of defending. Never show your hand first. By moving out of the way for a cross that never came, he allowed McGinn a free shot on goal and the Ulsterman didn't need asking twice to score.
Aberdeen's third came from a slick counter-attack but while Goodwillie took his chance well, he did find himself in acres of space because the man covering that flank, Paterson, had been caught out of position.
Not that Callum Paterson was the sole culprit for Hearts' defeat but his errors had the greater consequences.
However, others should not be let off the hook just because one player was slightly worse than the rest of his under-performing team-mates.
One example was the midfield as a whole who were second to everything.
Miguel Pallardo may have the excuse of not being match-fit after missing the start of the season through injury but that will not wash for much longer if he continues with this sort of display as he was chasing shadows from the first whistle to the last.
Prince Buaben, once again, did little to dispel the theory that he cannot play without his regular midfield partner Mongaro Gomis - whose absence these last two weeks has weakened the team. His return can't come about too soon.
Up front, there was one centre-forward who gave out a good lesson on winning the ball, holding up play to draw in other attackers and being a constant menace to the opposing defence.
Sadly for Hearts, that player was Aberdeen's David Goodwillie.
The Jambos' own targetman, Juanma, was sluggish in comparison and spent most of the time moaning to the referee instead of doing what he had been doing to better effect earlier in the season.
Aberdeen's defence gave an air of being well-drilled and organised. Each member of that back four not only knew what he was doing, but also what his colleagues were doing as well.
Hearts' back four resembled an out of tune jam in a folk music club's open mic session.
Then we come to the manager's performance.
Prior to the start of the season, I commented that Robbie Neilson no longer has the benefit of the 'surprise factor'.
Last season, many in the second tier did not know what playing style the then rookie manager was going to implement.
By the time they worked it out, Hearts had made a flying start and were cruising to promotion.
The top flight managers have had a year to study Hearts and some of them, Aberdeen's Derek McInnes in particular, looked to have found a way of containing them and exploiting any weaknesses in the plan.
I also mentioned before the start of the season of Neilson's need to find a plan B should A not work.
He has tried to develop one but it is clearly worse than the main scheme - namely, playing a striker like Osman Sow out of position on the left-wing is not a good idea.
Sow has clearly tried to adapt, and it is a credit to his professionalism that he has got on with the job asked of him.
But we all saw last season what he can do when played up front. He should be put back in that position with immediate haste.
Maybe playing him alongside Juanma could produce a fruitful partnership for Hearts? Because being dependent on one striker up front does somewhat limit your goalscoring opportunities.
Neilson also appears to have a little bee in his bonnet that won't buzz off.
Namely this obsession of having an attacking midfielder playing in between the centre midfield and the striker.
After all, when Neilson was a player for Hearts, this was a role that Paul Hartley executed to perfection.
The two players he has tried in this position since becoming manager have been Soufian El Hassnaoui and Gavin Reilly - unfortunately, neither have yet to show themselves as being anything like Hartley.
El Hassnaoui hasn't had the best of luck with injuries but when he did play, it was evident the team's rhythm was disrupted in order to accommodate him and only really started to flow when he wasn't selected.
Reilly meanwhile is finding the step up from second tier football to the top flight somewhat of a yawning chasm.
Premiership football is played at a faster rate of knots than in the Championship and Reilly has looked off the pace.
He may well adjust to it soon and show why Hearts signed him from Queen of the South in the summer but when other team-mates are not playing well, a passenger running out of puff and being out-muscled is the last thing the team needs.
Maybe going back to two up front and giving Reilly some breathing space to find his feet (and his build his stamina) - not to mention playing actual wingers (two from Jamie Walker, Billy King and Sam Nicholson) on the respective flanks themselves, could restore some balance to the team and make them into a more potent attacking threat?
Celtic at Parkhead are up next and a dramatic improvement is required all-round if Hearts are to at least make a game of it.
No doubt the club's official Twitter and Facebook accounts will be bombarding us with the usual faux-macho spin of "We go again" that they've been prone to doing after a bad result.
Only in order to go, you need to push down the clutch and shift the lever into first gear.
Because as Aberdeen so brutally showed at Tynecastle today, staying in neutral only ensures that an oncoming, title-chasing juggernaut will mow you down.
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