Both Oxford United and Fleetwood are keen to land the Blues striker this summer.
And The News understands the Blues would be prepared to listen to offers for the 27-year-old, who has a year remaining on his existing agreement after arriving from Ipswich Town for £425,000 in 2019.
Harrison is now fit again after injuring knee ligaments in February - and then playing on for another three games.
The Welshman will be ready to return for pre-season training after successfully completing his rehabilitation programme.
Oxford have already signed Ryan Williams after his Fratton exit this summer, and look ready to spend in a bid to reach the Championship.
A potential appeal of a move for Harrison will be partnering him with Matt Taylor at the Kassam Stadium.
The pair are close friends and have shown their effectiveness as a partnership in their time together at Bristol Rovers.
Fleetwood are also in the market for a striker and Harrison fits the bill for Cod Army boss Simon Grayson.
Cowley is operating with a reduced playing budget this summer, but knows any fees generated will be able to be ploughed back into his transfer kitty and bolster his spending power.
Pompey’s only signing so far has been teenage non-league defender Liam Vincent from Bromley.
Harrison has scored 16 goals in 70 appearances for the Blues, with 32 of those outings coming off the bench.
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