Jamie Paterson is attracting interest from Championship rivals Bournemouth and Queens Park Rangers.
The 30-year-old has missed Swansea City's last four matches due to his contract dispute with the club's owners.
Swansea - who value the former Bristol City man at £750,000 - have already rejected a pair of bids from QPR.
And it has emerged that Bournemouth have explored the option of adding the playmaker to their ranks.
However, the Cherries are closing in on a move for Norwich City's Todd Cantwell while they are also set to sign Cardiff City striker Kieffer Moore, meaning a swoop for Paterson appears unlikely.
Blackburn Rovers are also understood to have shown an interest in Paterson - who has registered eight goals and four assists in his 22 Championship appearances for the Swans so far this term.
But it appears increasingly likely that the price tag placed on Paterson will ward off potential suitors, which paves the way for the attacker to be re-integrated into the first team fold over the course of the coming weeks, barring any late deadline day twists.
Meanwhile, Swansea have been left frustrated in their pursuit of a left wing-back.
The club recently allowed Jake Bidwell - who was due to be out of contract in the summer - to seal a permanent switch to Coventry City.
It was hoped that they would get the green light to bring in a replacement for the 28-year-old, although confidence in bringing in a new face in that position has waned.
The Swans previously enquired about taking Josh Wilson-Esbrand on loan from Manchester City, although Pep Guardiola's side were reluctant to send the youngster out this month.
It is an area in which the coaching staff are desperate to strengthen in the final stages of the window, with a back-up striker also desired.
Swansea have explored the option of signing Nahki Wells on loan from Bristol City.
Russell Martin is keen to add a forward to his ranks, and Wells has stacks of Championship experience.
But a recruitment source told WalesOnline that "it won't happen" when asked about a potential swoop for Wells. He is expected to remain at Ashton Gate.
Elsewhere, Yan Dhanda is expected to leave Swansea on loan.
The transfer window closes at 11pm tonight.
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