But the Blues boss believes the in-form front man can become a Fratton hero by returning on loan next season.
And Cowley vowed he will do everything in his power to make that happen and fend off Championship interest in the Leicester City loanee.
After bagging 14 goals since November, the 23-year-old’s stock has risen with his form likely to have Championship suitors keeping tabs on his availability.
Cowley accepted it’s unrealistic to think Pompey could fund a permanent deal for Hirst, who is still contracted with the Foxes next season.
But he feels a return on another temporary stay could work out well for all parties.
Cowley said: ‘We’d love to sign George permanently.
‘We’re Portsmouth Football Club. These are the things we should aspire to do.
‘Realistically, though, I think that it’s beyond us.
‘It’s no criticism, I think it would be beyond the majority of League One.
‘On another loan, we’ve built a good relationship with George.
‘I know that he’s loved it here and he’s build a good relationship with the supporters and there’s a bond which has grown.
‘He’ll have some decisions to make in the summer.
‘Leicester will firstly have some decisions to make in the summer, and he will be involved in the decision making process.’
Cowley made it clear he believes Hirst has everything to gain by coming back to Pompey next season.
His form has seen him become a big fan favourite, and Cowley believes that status would be cemented if he returned to fire his team to the Championship off the back of regular football.
Cowley added: ‘We will do everything in our power to bring George back.
‘There will be some interest in the Championship for him, but he’s been in the Championship before and wants to play every week.
‘He wants to be a big part of something and he knows he’s loved here, his profile suits our game idea and gets the best out of him as a player.
‘For him it’s important because he’s at that age now where he must play every week and continue the upward curve of his development.’