The 22-year-old is training with Pompey, as he hopes to rediscover his scoring touch following a poor loan spell at Championship side Rotherham last term.
Hirst played 32 games, four of them as a striker, and did not score a single goal.
Rotherham were relegated to League One as well.
Per Leicestershire Live, he is now training with Pompey as he closes in on a loan move for the coming season.
Hirst impressed with England's youth teams and at the Sheffield Wednesday academy before his move to Leicester, but has not fulfilled his promise as yet.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!