Mark Catlin has told Jed Wallace he can fulfil his football ambitions by remaining with Pompey.
But the chief executive has warned the Blues will not be breaking their wage structure to keep him at Fratton Park.
Catlin revealed he has tabled two separate offers to the midfielder and his representatives in a bid to tie him to the club long term.
He insists the decision has now been left in the hands of Wallace, whose existing contract expires next summer.
There remain concerns, however, the in-form 19-year-old may instead opt to leave Pompey for a higher division.
As the scenario continues to play out, Catlin is adamant the club will not be putting pressure on the former Lewes man to sign.
Wallace, who is one of the lowest paid in the first-team squad, has consistently stated he is happy at Fratton.
But Catlin has stressed there will be no breaking the bank in negotiations.
He said: ‘Jed is a great lad and I have made my own views to him where I think his future lies.
‘He is a massive asset to the club moving forwards.
‘Short of putting a gun to his head and telling him to sign, there is only so much I can do.
‘It is down to him and his representative to make that decision and so far we have made him two separate offers.
‘I have tried to convince him his ambitions can be achieved here, he does not need to go anywhere else.
‘I genuinely feel going somewhere else for short-term gain could be a long-term mistake.
‘There are no deadlines put on him. He’s a Portsmouth player until the end of the season, come what may, and the last thing we want to do is put him under pressure.
‘But Jed knows there is only so much we can offer, there is only so much we can do, and I am definitely not putting the club in jeopardy again.
‘You break the bank for one and another three or four players will be knocking on the door.
‘It can set off a chain of events – so you have to stick rigidly with that.
‘With the greatest respect to him – and I want to see him stay – but the club has to come first. We have a limit.
‘We don’t want him bogged down with the contract scenario, so won’t be putting him under pressure.
‘As long as he is giving 100 per cent – which he is clearly doing – no-one can be upset with him.
‘But from now until the end of the season, in terms of the contract, the ball is going to be in his court.’
Wallace continues to be a popular draw for scouts, while reports have linked him with Stoke City.
But Catlin claims there has yet to be any approach.
He added: ‘There has been no interest – if there is it has not come to me.
‘I have not been contacted or made aware of anything.
‘I hope Jed makes the right decision and that would be to stay at Portsmouth.’