But the cost of funding a permanent deal for any of the players is looking likely to be prohibitive, at this stage – now leaving a loan as the most likely path to a switch.
Reports in Wales have suggested boss Russell Martin would be prepared to let the players leave in this window.
But that would come at a price with all three tied down to contracts.
Both Joseph and Whittaker have three years remaining on their agreements, while Cullen is tied down until 2024.
Pompey have said there’s transfer fees available for the right additions, but The News understands the only way permanent moves would presently accelerate for the Swansea players is if they were allowed to leave on free transfers.
That appears highly unlikely given the Championship’s financial commitment bringing in Whittaker and Joseph, along with the work developing Cullen through their ranks.
Whittaker arrived from Derby for a fee of around £700,000 in January last year, while Joseph came in from Wigan for an initial £500,000 last June.
Swansea hold a lengthy interest in Marcus Harness and the prospect of a player swap deal with the winger has been mooted.
Pompey want to recoup the £750,000 they paid Burton Albion for the winger in 2019, with the club’s most valuable asset looking likely to leave this summer.
Cowley was understood to want a permanent rather than loan stay for the Swansea players, but a temporary agreement is now looking the most likely route of travel if any move is to progress.
Pompey are, of course, without a senior striker to their name after returning to pre-season training.
Cowley’s keen on bringing back George Hirst after his successful loan stay last term, while a deal remains on the table for Aiden O’Brien.
Young Spurs talent Kion Etete is also high on the list of Pompey striking targets.