Speed and Exeter boss Paul Tisdale emerged as early front runners for the post once it was confirmed that Roberto Martinez would be leaving for Wigan but the Grecians released a statement on Wednesday insisting Tisdale will remain in the west country.
That leaves Sheffield United midfielder Speed in the driving seat to be handed the job and Yorath, who handed Speed his first Wales cap, believes he is the 'perfect man' for the task.
He told the Western Mail, "Gary Speed would be the perfect man to take over at Swansea. I have no doubts at all.
"Gary is a fantastic professional and is very-well respected in the game. As a player he achieved things at the very highest level so when he walks into a dressing room the players have respect for him straight away.
"If Swansea can get him I think it would be the right move definitely and a real coup for the club."