Pompey’s promotion rivals are keen on taking the striker to Hillsborough.
Harrison looks to be on his way from Fratton Park with Oxford United still keen on the 27-year-old.
The Blues will not let the £425,000 signing from Ipswich leave until they have a replacement lined up, however.
That doesn’t necessarily mean a like-for-like player coming in for the man brought in by Kenny Jackett in 2019, however.
Harrison didn’t travel to Fleetwood on Saturday for the League One opener, as Danny Cowley’s side picked up a 1-0 win.
The powerhouse front man has been laid low by coronavirus, and trained for the first time on Friday after recovering from the disease.
John Marquis got the nod to start up front at Highbury Stadium along with Gassan Ahadme, with new recruit George Hirst replacing Marquis with 16 minutes left.
Cowley is desperate to free up funds to get the players he feels are required to make his side competitive this season.
A bid for Michael Jacobs from Ipswich has been accepted, with the winger close to signing for Paul Cook’s side.
That will remove one of Pompey’s heavy hitters from the wage bill, with Harrison also among one of best earners among the current squad.
The former Bristol Rovers man will also command a fee, with his existing contract running until next summer.
Cowley has brought in 10 players so far this summer, with the head coach now focussing on bringing in midfield players.