Premier League giants City eased past Birmingham City with a 3-0 win in the last round, while Cheltenham needed extra time to overcome Mansfield Town 2-1.
The winners of this tie will take on either Swansea City or Nottingham Forest for a place in the quarter-finals.
City are in full stride heading into Saturday's cup tie after beating Aston Villa 2-0 on Wednesday evening to keep their incredible form going.
The Citizens have won nine matches in a row in all competitions since mid-December, the last five of those without conceding a goal.
Going further back, Pep Guardiola's men are without a defeat in 16 games and have won all but three of those.
Anything other than a routine victory this weekend seems unlikely, then, but Cheltenham will know that this competition has built a reputation down the years for producing upsets.
However, the Robins have lost all eight of their EFL Cup and FA Cup meetings with Premier League opposition, while City have won their last seven FA Cup games against sides from a lower division by an aggregate score of 26-4.
Cheltenham have at least made themselves tough to beat of late, going five without defeat in all competitions, albeit drawing the last four of those in the league.
Michael Duff's men are sixth in the League Two standings, three points off the automatic promotion spots after playing out a 1-1 draw with second-place Newport County on Tuesday.
After beating South Shields, Crewe Alexandra and Mansfield in the first three rounds, Town are now aiming to reach the FA Cup fifth round for just a second time in their history, last doing so in 2001-02.
City are no strangers to going deep into the competition, of course, reaching the fifth round in each of the last five campaigns and last losing at this stage against Middlesbrough in 2015.
With Duff describing this tie as the "greatest free hit in history", Cheltenham are out to pull off what would be the greatest upset in the famous competition's recent history.
Cheltenham Town FA Cup form: WWW
Cheltenham Town form (all competitions): LDDWDD
Manchester City FA Cup form: W
Manchester City form (all competitions): WWWWWW
The games keep on coming thick and fast for City, with West Bromwich Albion and Sheffield United to come next week in the Premier League.
Guardiola takes each cup competition seriously, but this is realistically the only chance that he will have to give his first-team regulars a little breather.
Sean Long is back in contention after shaking off an injury issue, but Duff could stick with a similar XI to the one used against County.
Cheltenham Town possible starting lineup:
Griffiths; Raglan, Tozer, Boyle; Blair, Clements, Azaz, Sercombe, Freestone; Lloyd, May
Manchester City possible starting lineup:
Steffen; Cancelo, Harwood-Bellis, Laporte, Mendy; Doyle, Fernandinho, Silva; Torres, Jesus, Palmer
We say: Cheltenham Town 0-3 Manchester City
Even accounting for the changes Guardiola is expected to make this weekend, it is difficult to see past anything other than a routine away victory.
Cheltenham are unbeaten in five matches, but City have won nine in a row and will surely keep that run going at Whaddon Road on Saturday evening.