The Blades have had a dismal Premier League campaign to date but beat Bristol Rovers 3-2 in the last round, while Plymouth saw off Huddersfield Town by the same scoreline.
The winners of this tie will take on either Millwall or Bristol City in the next round.
United's win over Rovers in the last round was their first victory in any competition this season at the 22nd attempt, with Omar Bogle scoring what proved to be the winning goal in an entertaining tie at the Memorial Stadium.
However, normal service was resumed at the weekend as the Blades went down 3-1 to Tottenham Hotspur, leaving them bottom of the Premier League and 11 points from safety.
The immediate aim for United will be to better Derby County's lowest-ever points return of 11 in the Premier League era, but the FA Cup does at least provide them with a welcome distraction.
With Plymouth and then either Millwall or Bristol City standing between them and a place in the quarter-finals, Wilder may well be tempted to field a strong lineup on Saturday afternoon.
The same is true for Argyle, who enter this game on a good run of form thanks to three wins and a draw in their last four matches in all competitions.
Ryan Lowe's charges won 2-1 away at Sunderland on Tuesday to move up to 11th in League One, six points adrift of the playoffs.
Plymouth have already come through three rounds in the FA Cup, meanwhile, having knocked out Charlton Athletic, Lincoln City and Huddersfield to make it this far.
They are now looking to reach the fifth round for the first time since 2006-07, though this is just their second appearance in the fourth round since then (also 2007-08).
This will of course be a tough test against top-flight opposition, though, and United have won 15 of their last 16 FA Cup meetings with sides from a lower division.
Sheffield United FA Cup form: W
Sheffield United form (all competitions): LLLWWL
Plymouth Argyle FA Cup form: WWW
Plymouth Argyle form (all competitions): DLWWDW
Wilder should field a fairly strong XI on Saturday, however, with John Egan - suspended for the Blades' next league game - among those in contention to start.
Rhian Brewster may get the nod up top as he looks to improve on a poor return of zero goals in 15 appearances since joining from Liverpool last summer.
Panutche Camara missed the win over Sunderland through suspension, but the midfielder is back involved for this one.
Striker Luke Jephcott has been involved in a goal in each round of the FA Cup so far this term, scoring two and assisting another, and will lead the visitors' line at Bramall Lane.
Sheffield United possible starting lineup:
Ramsdale; Basham, Egan, Ampadu; Bogle, Lundstram, Norwood, Fleck, Lowe; McGoldrick, Brewster
Plymouth Argyle possible starting lineup:
Cooper; Aimson, Opoku, Watts; Edwards, Camara, Fornah, Mayor, Grant; Jephcott, Hardie
We say: Sheffield United 3-1 Plymouth Argyle
Plymouth knocked out Championship opposition in the last round and will now be looking to claim the scalp of a Premier League side.
The League One outfit enter this game in decent form, whereas United have won just two matches all season, but we are still backing the hosts to come out on top assuming they field a strong side.
Top betting tip
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