The forward has been very impressive for the League One club in recent weeks.
The 23-year-old had a tough start to his loan spell, but has now found his groove, impressing the fans and his manager.
"It would be up to the club to decide what is affordable," Cowley told portsmouth.co.uk.
"If we were able to sign George Hirst, I would strongly recommend it. I've said that from the beginning.
'These are the type of young players I think we should be really trying to sign at Pompey.
"We speak to Leicester on a regular basis, and we're really appreciative they allowed us to take George, and I've been really proud of him and the way he's worked.
"Like all young players, success doesn't always happen in a straight line and he's really had to fight to get to this moment."
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