The Swans chairman has revealed that his shortlist for the managers role at The Liberty Stadium has now been reduced to about six candidates with Gary Speed and Aidy Boothroyd believed to be amongst those tipped to succeed Martinez who finalised his move to take over the managers post at Wigan on Monday night.
"We are down to about six main people," Jenkins has told BBC Sport.
"I know in my mind who we're looking at but I'm not going to give names.
"Hopefully it will push on between now and the weekend."