The kick-off times for both matches are to be confirmed.
FA Cup doubt
However, the Old Trafford fixture is subject to both clubs' participation in the FA Cup sixth round, which also takes place that weekend.
Man Utd visit Derby County on Thursday 5 March, and Sheff Utd travel to Reading in the FA Cup fifth round the day before.
If either, or both, progress - the ties will be decided on the evening - their meeting on 22 March will be postponed.
The two teams' Premier League matches after the first legs of their round-of-16 UEFA Europa League fixtures are already scheduled for Sunday, so do not move.