Swansea City expect Ryan Manning, Joel Latibeaudiere and Kyle Naughton to leave the club when their contracts expire this summer.
Martin had been due to hold talks with Swansea’s American owners in Washington DC over his own future at the club this week.
However, the former Scotland international has not travelled across the Atlantic and is in the frame to replace Ruben Selles at St Mary’s Stadium.
Swansea confirmed in its retained list that Manning, Latibeaudiere and Naughton are expected to become free agents next month, although it remains possible that not all three depart.
‘Sad to lose them’
Speaking ahead of Swansea’s final day win over West Brom, Martin said of the trio: “I’d love to keep all three, but we’re not at that point at the moment.”
He added: “I’ll be really sad to lose one of them, let alone all of them.”
Republic of Ireland international Manning registered 10 assists and five goals in the 2022-23 Championship campaign. He also won the club’s Supporters’ Player of the Season award.
Naughton has made more than 250 appearances for Swansea since joining from Tottenham in 2015 while Latibeaudiere has been a prominent figure under the current coaching staff.
Michael Obafemi will complete a permanent transfer to Burnley following the conclusion of his loan spell at Turf Moor.
Goalkeeper Andreas Sondergaard will also leave the club at the end of the short-term deal he signed when joining in February 2023.
Academy products Tivonge Rushesha and Daniel Williams, who have both made senior appearances, are to depart when their contracts expire this summer.
At academy level, Josh Carey, Richard Faakye, Zane Myers and Evan Watts have all been offered professional contracts.
However Geoffroy Bony, the son of former Swansea and Manchester City striker Wilfried Bony, along with Sam Leverett, Tarrelle Whittaker, Corey Hurford, Jada Mawongo, David Roberts and Wasiri Williams are to leave.