The 37 year old, who is now in his third spell with the club has played a total of 268 (+ 2 as sub) games whilst netted a total of 118 goals in a six year period.
Deano, Deano, Deano
The move comes following an unsuccessful spell in the A-League with Australian side Perth Glory where he participated in six games and failed to score in any.
Blades boss Neil Warnock told sufc.co.uk; "Brian is not fully fit yet because he has not done any training since returning from Australia and will do some work with Tony Daley but I feel he maybe able to contribute.
"Even if we do sign another striker in the January transfer window, we feel that Brian, especially with his affinity to the club, will be useful to have around until the end of the season."