If Sharp agrees a move to the Blades it would be be the 29-year-old's third spell at the club.
He has previously worked under current Bramall Lane boss Nigel Adkins at Scunthorpe, Southampton and Reading.
Sharp started his career with Sheffield United before joining the Iron in 2005, only to return in 2007, and has made 66 appearances for the club.
Head coach Uwe Rosler admitted that Sharp had just been left out of the team on Tuesday and had no injury problems.
Talks had been ongoing between the Blades and United and Sharp's agent and the player's return home would indicate that an agreement has been reached between all parties.