Amos, 27 has been told by newly promoted Bolton Wanderers to find a new club after he was left out of their pre-season tour to Scotland. He lost his number one spot twelve months ago when the Trotters signed former Blades stopper Mark Howard.
The keeper, who began his career with Manchester United, spent most of last season on loan at Cardiff City after being deemed surplus to requirements.
Blades boss Chris Wilder has stepped up his search for a keeper following the injury to Simon Moore at Rotherham United last Friday night. Academy starlet Jake Eastwood has since stepped in, and produced good performances in the win at the New York Stadium and in last night's friendly with Stoke City - both resulting in a 2-1 victory.
Recently, Middlesbrough's 37 year old stopper Dimitrios Konstantopoulos has been linked with a move to Bramall Lane, but Amos would prove to be a likely target.