Former Rangers winger Barrie McKay remains the most likely recruit and discussions with the 26-year-old free agent, who exited Swansea City in June, are ongoing.
"There's nothing done, no contract has been put in front of him. He wants to see his options and then come back to us,” explained sporting director Joe Savage.
“We all think Barrie is a very good footballer. If we can, we will try to do something. I know he's got interest in England so it's just a matter of trying to negotiate.
“That's the type we want. We want quality players like Barrie McKay and if we can get him then brilliant. If not, I'd like to think it shows the standard and the quality we are trying to bring to the club. We look at Barrie and think he will come in and impact the starting 11. That puts more pressure on the boys there just now and that's the quality we need to get to where we want to go.”
There is scope for more to follow, with Savage refusing to rule anything out should a gem of a free agent present itself. Having off-loaded some of the makeweights during the summer, if the right options become available, he says the club could be persuaded to do more business.
"I don't think you ever close up on that. We won't be desperately seeking but we will keep an eye on it to see if there is anything we feel is worth taking.”
If not, they are willing to wait until the market opens up again in January, or even the summer as they chase proper targets rather than panic buys.
Selling the club to targets is something the Gorgie hierarchy have become adept at, from sending a welcome pack to players and their agents, showing them a video highlighting the history, the traditions, the support and the ambition, to tours of the training facilities and the ground before cashing in on the castle and the capital city backdrop as they look to clinch the deal over lunch.
But, Savage knows that a different approach is required when it comes to extending contracts and convincing assets like John Souttar that there is good reason to sign a fresh deal.
“He's been here so long , he knows the history of the club and the tradition. We're trying to negotiate with John and get him to sign a new contract, but John's a sensible lad with a good family behind him and he understands exactly what he's looking for. We're trying to come up with something we think John would accept. So far it's just been initial conversations. He's spoken to Robbie and I've spoken to his agent and we'll see what we can do.
“We'll try and we'll try and we'll try and we won't stop until he tells us to leave him alone. He's not done that yet and I don't think he will because he's not that type of character. He's enjoying himself here and is doing really well. But we all have to understand that he has just returned from a big injury and he has to make sure he's doing the right thing for him and his family."
That awareness of just how fickle fortunes can be may mean that big-money switches are even more tempting, Or, having fought back from injuries, he may feel like he has unfinished business at Tynecastle, as he attempts to put the past couple of seasons behind him and reassert his international credentials.
For now, though, Hearts have made it clear that they are willing to risk losing the 24 year-old defender for nothing rather than accept a few bawbees now.
"We did knock back two offers from a Championship club that didn't meet our valuation in any way whatsoever. If that means he leaves next summer on a free transfer then so be it but, hopefully, by then we've either persuaded him to stay or we've finished first, second, third or fourth in the league or done well in the cup and he would leave with our best wishes.
“John's a Rolls Royce of a centre back, isn't he? He's a top, top player. If he'd played another ten or 15 games he probably would've been in the Scotland squad. We value and rate him that highly which is why I don't want to be disrespectful to the team that made the bid but it was nowhere near and we're happy to keep him.
“He can't talk to anyone about a pre-contract until the first of December so it's now up to Robbie and I over the next two or three months to absolutely batter him - not physically - to get him to sign a new contract."
As they work to bring in young, hungry players, with a point to prove and, ultimately, a decent sell-on value, the club is keen to tie up their best talent on long-term contracts to dull the pain if they do find a new challenge.
“If anyone does want to come in for them then we're in the driving seat. We can turn round and say we expect x-amount to sell them and we're doing that with John, even though he's in the final year of his contract. I wasn't here with the Callum Patterson and Aaron Hickeys of this world but it's easier said than done.
“We don't want John to leave and we're trying our best to keep him here but we're not ones to hold grudges. If he gets an offer he feels he can't turn down then sometimes there's nothing you can do."