The 42-year-old could be about to make a return to the Swans to take up the vacant managerial role after Latics chairman Dave Whelan gave the go ahead for talks
Jones left Swansea in 2009 to join Roberto Martinez as the Latics No.2 but the Welsh club are now without a boss, with Brendan Rodgers' move to Liverpool set to be confirmed on Friday.
And Wigan chairman Dave Whelan has now allowed Swansea to negotiate over Jones' return as Rodgers' successor at the Liberty Stadium.
"I spoke to Roberto and we gave permission virtually immediately," Whelan told Sky Sports News.
"Roberto, like me, does not believe in holding people back.
"Graeme is a good lad and if he does go we will miss him immensely. They have been a great partnership for quite a while."
Whelan suggested Jones would be keen to accept the opportunity at Swansea, should it be offered to him, adding: "He is ambitious. He is football through and through and is up for the challenge."
“We got him from Swansea so it's only fair we let Swansea speak to him if they want to."
Jones turned down the Swans in 2010 prior to Rodgers' appointment, when Paulo Sousa left the club after a disappointing season in the Championship.
Blackpool’s Ian Holloway and Brighton’s Gus Poyet have both also been strongly linked with the job but betting has been suspended since 42-year-old emerged as the favourite.
Jones spent just over two years at Swansea as Martinez laid the groundwork for the passing style which has earned the club plaudits during their maiden Premier League campaign.