Speed, 39 arrived at Bramall Lane in a £250,000 deal from Bolton Wanderers on 1st January 2008, making his debut on the same day in a 0-0 draw at Wolverhampton Wanderers - but currently has one year left remaining on his player/coach contract at Bramall Lane.
The 86 capped Welsh international is due to have talks with Swansea City chairman Huw Jenkins on Monday about replacing Roberto Martinez who left the club last week to take up the role of Wigan Athletic manager. "As things stand, there's some good people who have applied. We are going to push on next week and get cracking." Jenkins told BBC Sport.
There are of course other names who have shared their interest in becoming manger; Aidy Bothroyd, Dennis Wise and Gus Poyet are also believed to be interested.