The Championship side are looking at potential deals which could see the winger move to the second tier.
The News understands the possibility of a player swap agreement which could see Harness depart has been explored.
Pompey are keen to recoup the £750,000 they paid to bring in the 26-year-old from Burton Albion in 2019, however.
It appears increasingly likely Harness will be on his way this summer, after the Blues took up an option to extend his existing agreement by another 12 months.
That ensured the Coventry-born talent would not be leaving for free after his deal came to a close.
It appears all parties feel the time is right for Pompey’s most bankable at present to move on, however.
A player swap move with Swansea does raise the prospect of some intriguing options for Danny Cowley.
The Londoner is a fan of the likes of attacking duo Morgan Whittaker and Kyle Joseph, with reports in Wales this summer suggesting Russell Martin would be prepared to let both men depart.
Pompey’s preference would be to sign those players on a permanent deal if a move was to gather pace.
Meanwhile, Cowley has again been linked with a move for striker Liam Cullen who spent the second half of last season on loan at Lincoln.
Harness was among the first-team group as they reported back for pre-season training today.
The players undertook testing this morning before being put through an afternoon session at their Roko training base.
Cowley is looking to reshape his options this summer, with Pompey currently not having a senior striker at their disposal.
The Blues are understood to be prepared to let Ronan Curtis depart, with a £500,000 fee sought for the Republic of Ireland international.
Pompey have yet to complete any signings with the summer transfer window opening on June 10.