Celtic keen to contact Martinez
"I had a call off their chief executive (Peter Lawwell) making me aware that they'd like to talk to Roberto," Swansea chairman Huw Jenkins told BBC Wales.
"Like I've always done I refused that until I've spoken to Roberto myself and talked things through."
Martinez, 35, took Swansea into the Championship and steered them to eighth place last season, just missing out on the playoffs.
Jenkins said he would not stand in the way of Martinez, who has been linked in the media with Premier League club Wigan Athletic, if he wanted to consider the Celtic job.
Strachan quit Celtic last month after the club just failed to land a fourth consecutive league title.