Swansea manager Roberto Martinez is expected to discuss Celtic's approach with his employers when he returns from holiday later on Wednesday.
Celtic's initial request to interview Martinez was rebuffed but Swans chairman Huw Jenkins has admitted he will not stand in the Spaniard's way if he insists on meeting Parkhead chief executive Peter Lawwell.
The 35-year-old appears destined to do so after apparently saying "any young, aspiring manager with ambition would be interested in a job like that."
But Wigan's impending managerial hunt could scupper any hopes Celtic maintain of luring the former Motherwell midfielder, who led Swansea to the Coca-Cola League One title in his first full season and then eighth place in the Championship.
Wigan manager Steve Bruce is negotiating personal terms with Sunderland and the compensation package from that deal would cover the four years remaining on Martinez's Swansea contract.
Latics chairman Dave Whelan has already admitted Martinez, a celebrated former Latics player, would be at the forefront of his thoughts when he begins moves to replace Bruce.
Meanwhile, a Celtic source has dismissed claims that Tony Adams is in the frame for the job as "complete garbage".
The former Portsmouth manager claimed former Hoops boss Wim Jansen was ready to take him to Parkhead if the Dutchman returned as technical director.
Adams told talkSPORT: "My good friend Wim Jansen is probably in at Celtic. It would be him as technical director and me as manager."
The former Arsenal skipper added: "I've not applied for the role. I know Wim Jansen, who has put me in there."
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