The Owls are bidding to reach the quarter-finals for the first time since 1996-97, when they were a top-half Premier League side.
Pep Guardiola's Manchester City won both domestic cup competitions last season, and were FA Cup semi-finalists in 2016-17.
Wednesday have already knocked one Premier League side – Brighton and Hove Albion – out of the competition.
The sides last met in the 2014-15, when a 90th-minute James Milner goal, his second of the game, took the Citizens through. It was much tighter than their League Cup meeting that season, a 7-0 win, also at Eastlands.
The Blades will be strong favourites against Reading or Cardiff, both in the lower half of the second tier. Sheffield United's away form has been one of the highlights of their first season back in the Premier League.
They won 2-0 at the Madejski Stadium last season, but lost their last trip to the Cardiff City Stadium, 2-0 in August 2017.
The Blades have not reached the quarter-finals since 2014, when they progressed to the semi-finals.
Wolverhampton Wanderers are the only team above Sheffield United to have been knocked out of the competition, but at least one more will miss out on the semi-finals, with Liverpool due to travel to Chelsea if they overcome a replay with Shrewsbury Town.
This year is the first where there will be no replays in the fifth round as the Football Association bows to pressure from the clubs who compete in Europe to ease their over-congested fixture lists. Liverpool's fourth-round replay will take place during the time designated as their mid-season winter break.
Replays had already been scrapped from the quarter-finals onwards.
In another change to the competition, the round will be played in midweek, in the first week of March.
Meanwhile, Owls goalkeeper Cameron Dawson has signed a new contract which will keep him at Hillsborough until the summer of 2024.
The former youth international has established himself as the first-choice goalkeeper this season, displacing Keiren Westwood.