Bruce, 25 is the son of former Blades player and manager Steve Bruce and has been deemed surplus to requirements by Ipswich Town and has also been transfer listed by Roy Keane.
He was linked with a move to Bramall Lane three years ago (see link below) when then manager Bryan Robson was keen on the defender but opted to stay at Portman Road.
Blades boss Kevin Blackwell has only two centre-halves at his disposal in captain Chris Morgan and new signing Johannes Ertl and whilst he play other players in that position the manager is eager to bring in new players.