John Toshack believes that Gary Speed would make an ideal candidate for the Swans job
The former Swansea City and current Wales boss was talking to the BBC about the various merits of some of the people linked with the job vacated by Paulo Sousa on Sunday evening.
Toshack told BBC Sport "Gary (Speed) has been around a long time but hasn't been the number-one man yet
"Maybe now is the right time for him, he would know the area, he's Welsh... so maybe if he was approached.
"If the people at Swansea felt that would be the right choice, well I think maybe it's the time for Gary now to go in and be his own man
"But he's at Sheffield United at the moment and we don't really know what his thoughts are.
"Chris (Coleman) has got experience of management, obviously things didn't go too well for him at Coventry if we're honest
"His [previous] job, at Real Sociedad in Spain, he was the victim of very, very difficult circumstances there, it was virtually impossible for him to carry on."
Toshack though insisted that the Swans were in safe hands until any appointment was made
"Colin Pascoe and Alan Curtis... are very capable lads, Swansea lads through and through," Toshack said.
"So hopefully they'll be able to get on with things, keep the players ticking over at this time of year.
"But Swansea need to be thinking about making an appointment as soon as possible; I wouldn't rule out them letting those two get on with it for a while to be honest, stranger things have happened.
"The difficult thing with this is the timing of it, just back in training now.
"Normally... you've got your pre-season plans set and ready, and for this to happen to Swansea again right at the beginning of it obviously throws [the club into disarray].
"For the chairman as well, who I know has worked very, very hard there, the way the last two managers have gone - Martinez and Sousa - will have been a little bit disappointing for them."