They have turned their season around after a remarkable run of form under new boss Paul Heckingbottom. Unbeaten since October at Bramall Lane, they moved back into the top six at the weekend with a 2-0 victory over neighbours Barnsley.
The biggest threat to their promotion ambitions this season is surely their mounting injury list, which has seen the entire right side of their defence decimated and a number of strikers ruled out for varying lengths of time.
United looked at free agent Andre Wisdom but decided against signing him, although Heckingbottom admits United are “serious” about bringing a free agent in.
So we scoured the free agent market to pick out 12 players who could possibly do a job for United – click through our photo gallery to have a look ...
5. Yaya Sanogo
Formerly of Arsenal, Sanago is a France U21 international and left Huddersfield last season. Also played on loan at Charlton and has experience of English football Photo: Stuart MacFarlane
6. Martin Cranie
A player well-known to Blades supporters, after his short spell helped get United over the line the last time they were promoted to the Premier League. He’s now 35, but could he do a similar cover job again? Photo: Nathan Stirk
7. Zeki Fryers
An option for the left of defence, where United are also quite weak with Enda Stevens, Jack O’Connell and Ben Davies out injured. Can also cover left-back and has decent pedigree, formerly of Manchester United and Spurs Photo: Dan Mullan
8. Shaun Cummings
Formerly of Chelsea, Reading and Millwall, Cummings is a right back who can also play right wing-back, but has been out of the game for a long time and may take too long to get up to speed Photo: Pete Norton