Nigel Clough's men stunned Premier League side Aston Villa in the third round, earning a 2-1 win at Villa Park thanks to goals from Jamie Murphy and Ryan Flynn.
That result has done little to boost United's league form, though, and they sit just outside the relegation places in 20th place after winning just one of their last six.
However, the Yorkshire club face another out-of form side in Fulham, who are just a point above the drop zone in the Premier League following a 4-1 loss to Sunderland a 2-0 defeat to Arsenal.
Rene Meulensteen's men needed a replay against Norwich last week to secure a place in the fourth round, but the Dutchman will have been pleased with his side's performance in that clash, which ended in a comfortable 3-0 victory at Craven Cottage.
The London outfit will be expected to replicate that display against their third-tier opposition and seal a first win at Bramall Lane since 1985.
Defender Fernando Amorebieta is Fulham's only absentee for the game, with the Venezuela international unavailable because of a knee injury.
United, by contrast, have a number of players ineligible as midfielders Elliot Whitehouse and Callum McFadzean, as well as striker Billy Paynter, all miss out.
However, Clough's squad has been boosted by the arrivals of defender John Brayford and attacking midfielder Stefan Scougall, who joined on Friday from Cardiff City and Livingston respectively.
Former Derby boss Clough believes United can spring a second successive upset, but accepts that the odds are against them.
"There's no reason why we can't (cause another upset), but it will be a little more difficult this time," Clough told the Sheffield Star.
"We've got to remember they're two divisions above us and the quality they have throughout their squad of 25."
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