Celtic have made an official approach to appoint Swansea manager Roberto Martinez.
The SPL giants are searching for a replacement after Strachan left the club last Monday.
The Bhoys have been linked with Owen Coyle, Tony Mowbray, David Moyes, Craig Levein and Mark McGhee amongst others.
“I had a call off their chief executive making me aware that they'd like to talk to Roberto,” Swansea chairman Hue Jenkins told BBC Sport.
“Like I've always done, I refused that until I've spoken to Roberto myself and talked things through.”
He added: “I think you've got to respect that type of club Celtic are and what opportunities exists - perhaps not in the League but certainly in the Champions League - and the size of the club.
“Naturally, I suppose that interest would require anybody to sit and consider their position.
“It's basically up to him how he sees it, I think there's certainly no possibility in us forcing any issue. Roberto has got to consider his future and where his commitment lies.”
Martinez steered the Welsh side into an eighth-place finish in The Championship last season after winning League One in 2008.
The former Real Zaragoza midfielder has experienced Scottish football before having spent a short spell at Motherwell in 2001.