Bakary Sako could make a prompt return to Crystal Palace but Roy Hodgson does not expect Jason Puncheon to make way for him.
The forward remains a free agent having left Palace at the end of last season and he has been offered a new contract at Selhurst Park, though two players would first have to leave to satisfy Premier League rules before he is able to sign.
Puncheon remains a target for Middlesbrough, Ryan Inniss is nearing a loan move to Dundee and Sulley Kaikai could also move on loan to Brentford. The former also impressed in midfield in Tuesday's Carabao Cup victory at Swansea.
Hodgson said of Sako: "We offered him a new contract, despite the fact we couldn't be certain he would be fit enough for the start of the season.
"He turned that down, but (sporting director) Dougie Freedman has told me he has now been contacted by the player and his agent and that they may have rethought that. If that is the case, then we will review it, but we can't sign anybody unless two players leave.
"Ryan Inniss is likely to leave (for Dundee), but we would still have 25 squad players of the necessary age, so we can't sign another as it stands.
"(Sako) perhaps thought he could do better elsewhere. We like him and he likes us, so I don't have any problems if a gap presents itself, I would be happy to see him back."
Puncheon missed the second half of last season with a knee injury and in his absence Hodgson has developed a settled team in which Luka Milivojevic has consistently worn the captain's armband.
But the manager said: "Puncheon is still a Crystal Palace player. He'll be a Crystal Palace player until a club comes in and persuades him and us it is a good idea that he leaves.
"I have no desire to thrust any player out of this club. I have sympathy for Jason, who last year didn't play many first-team games, and the competition where he plays is strong and we both know that.
"He played at Swansea and was really, really good, so he showed he still has the ability to play at the level we want him at. But I wouldn't necessarily stand in his way if a good opportunity came along.
"Whoever it is that wants him had better move quickly."
On Saturday Palace host Southampton, the team that ensured Hodgson's managerial reign as Eagles boss began with a 1-0 defeat.
Ahead of the coming international football break, he said: "We would like a win before it, but you can't put yourselves under that pressure of a 'must-win' game.
"We think we know most of their players and the type of game that they play. There is nothing to particularly talk about with surprises, but we know how they play, and they know how we play."