Speed, 38 is a former Welsh international and is expected to join the Blades on 1 January when the transfer window opens - initially on loan before making a permanent move and will make his debut at Wolverhampton Wanderers' Molineux Ground..
He was made Player/Coach by former boss Sammy Lee at the Reebok Stadium and has since stepped down following the dismissal of Lee and the appointment of Gary Megson.
He said: "I'm not in the team at Bolton. I've no complaints about that, the team are playing well but I need to be playing games.
"I will see what happens. I am fit enough to play. I have not got much time left and I want to play football."
Speed's team mates Stelios Giannakopoulos and Ivan Campo have both been linked with moves to Bramall Lane and could soon join Speed next month.