But the Blues face a nervous wait to see if any clubs swoop to sign the Leicester City striker this summer.
The News understands Hirst has told Cowley he wants to come back for a second season at Fratton Park, after being embraced by the Fratton faithful.
It appears Leicester club are either likely to sell the 23-year-old, or extend his contract and send him out on loan once more next term.
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The Foxes will run the rule over Hirst when he returns for pre-season training at the end of this month.
Brendan Rogers will then have to decide the path forward for the powerhouse, who made a big impression over the second half of the season at Fratton Park.
There appears to be little hope of Pompey being able to fund a permanent deal for Hirst.
Even with a year remaining on his deal Leicester still have a sizeable valuation attached to the striker, after he was signed by their Belgian sister club Belgian side OH Leuven following a controversial 2019 move from Sheffield Wednesday.
The concern for Pompey would be a Championship outfit or one of the wealthier League One sides swooping for the man who bagged 15 goals last term.
Cowley remains clear on his position over Hirst returning, however.
He said: ‘We’d love to have George back.
‘We’re really respectful of Leicester and know he goes back and will train there in pre-season.
‘They will rightly get a good look at him and hopefully see the progress he made.
‘I know that they are pleased with the way we looked after him and the work we did with him, so that gives us satisfaction clubs know their players will be looked after here.
‘We’d love to have him back but ultimately that will be a decision made firstly by Leicester City and then George and his representatives.’
Hirst’s progress at Pompey proved one of the stories of last season, as the England under-20 international overcame a difficult start to make a strong impression at PO4.
It took until November for his first goal to arrive, as he took time to settle after arriving off the back of injury issues.
Cowley believes the front man deserves recognition for showing resolve to bounce back from a difficult start, off the back of a tough loan stay with Rotherham.
He added: ‘The way he developed in our environment last season, he takes a lot of credit for that.
‘I was so proud of the resilience he showed and how hard he worked.
‘From a coaching perspective, to see young players work really hard and get their reward is pleasing.’