Wigan assistant manager Graeme Jones has been given permission to talk to Swansea, Latics chairman Dave Whelan has confirmed.
The Swans are beginning the hunt for a new manager after agreeing a compensation deal with Liverpool to allow Brendan Rodgers and backroom staff members Colin Pascoe, Chris Davies and Glen Driscoll to move to Anfield.
Whelan told Sky Sports News: "I had half a dozen phone calls saying Swansea were wanting permission to talk to Graeme and I said I really don't know because our chief executive (Jonathan Jackson) was in a Premier League meeting. But he rang me at 2.30 and said that was the case and we gave them permission immediately."
Rodgers will be officially unveiled as Liverpool manager at a press conference on Friday morning and Swansea chairman Huw Jenkins had made it clear that the club would move quickly to find the Northern Irishman's successor.
And Latics number two Jones, who worked with Roberto Martinez at the Liberty Stadium between 2007 and 2009 before following the Spaniard to Wigan, appears to be in pole position after being granted permission to speak to Swansea.
Whelan said: "Roberto doesn't believe in holding people back. It's a free country but if he goes we'll miss him immensely. He's ambitious, has played for us and is a football man through and through.
"He's worked with Roberto for a few years but I think he's up for the challenge and is a very good lad. Roberto would like him to stay - they've been a great partnership for quite a while and the first thing Roberto said was he'd miss him immensely.
"But you can't stop progress and it's unfair to say 'you can't take that job, you're under contract'. It's not fair."
The likes of Brighton boss Gus Poyet, Blackpool's Ian Holloway and Birmingham's Chris Hughton were all among the favourites for the Swansea job, but Jones emerged as the clear favourite following a flurry of bets that led bookmakers to suspend betting.
Jones, 42, was previously approached by the Swans before they appointed Rodgers in 2010 in the wake of Paolo Sousa's departure. The former striker, who has only previously worked as an assistant manager, was a popular figure during his previous spell in south Wales.