Exeter boss Paul Tisdale has emerged as a front-runner for the Swansea job.
Swans chairman Huw Jenkins has a list of applicants that now tops the 100 mark, with Tisdale's odds having been dramatically shortened since the weekend.
He is now second favourite behind Graeme Jones, who is expected to join Roberto Martinez at Wigan as assistant manager and Jenkins has hailed Tisdale`s record of successive promotions with the Grecians was "remarkable".
However, a club statement on Exeter's official website played down any moves, saying: "Although potential opportunities may be attractive, Paul believes the opportunity afforded to him three years ago by Exeter City football club will always be the most important one he has been given.
"Every effort is being made by Exeter City to grow the business to enable Paul to continue the significant improvement the team has made recently."
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