The winner of the match will face either Bristol City or Aston Villa in the last 16 - here is our preview of the game.
There are no fresh injury concerns for Stoke, so the team could be similar to that that saw off Wolverhampton Wanderers in the second round, meaning starts for the likes of Nathan Collins, Lee Gregory and Harry Souttar are possible.
Joe Allen and Thibaud Velinden are long-term injury absentees, whilst the game is likely to come too early for Ryan Shawcross’ return. John Obi Mikel and Steven Fletcher should be fit enough to feature.
Dominic Samuel could make his second debut for Gillingham after joining the club on Monday. The forward scored seven times in 25 appearances during a loan spell in the 2015/16 season, but Gillingham manager Steve Evans has commented he is unsure if Samuel will travel with the squad for the game.
The Gills will be without cup tied Josh Eccles, as well as injured duo Kyle Dempsey and Stuart O’Keefe, leaving Evans with 18 fit first team players to choose from.
Both teams are expected to make plenty of changes from their recent league fixtures.
Predicted line ups
Stoke (possible 3-5-2): Davies - Souttar, Collins, Martins Indi - Smith, Oakley-Boothe, Thompson, Tymon, McClean - Gregory, Fletcher.
Gillingham (potential 4-3-3): Bonham - McKenzie, Tucker, Medley, Ogilvie - Woods, Robertson, Willock - MacDonald, Akinde, Coyle.
Stoke saw off Blackpool and Wolves to reach this stage of the competition, but are struggling with their league form, picking up a draw and a loss from their opening two games.
They have kept three clean sheets from their four competitive games this campaign, but have scored just one goal themselves.
Gillingham reached the third round after wins against Southend United and Coventry City, and picked up their first league victory of the season on Saturday - 3-2 away to Wigan Athletic. They have won four of their five competitive games this season.
Ones to watch
Steven Fletcher could come into Stoke’s starting lineup after impressing from the bench in recent outings. He will be looking to put in an impressive shift to prove he is fit enough and can lead the line for Michael O’Neill’s side this season.
Samuel is certainly one to keep an eye on if he features for the Gills, but John Akinde has a point to prove up top, now finding himself behind both Samuel and Vadaine Oliver in the pecking order of forwards at the club. He is in line to start here, and could do with a goal or two.
The last time the two teams met was in the FA Cup in 2012, when Stoke ran out 3-1 winners thanks to goals from Jonathan Walters, Cameron Jerome and Robert Huth.
The last time the two teams faced off in league action was in the 2004/2005 Championship season - Stoke won 2-0 at home before losing 2-1 at Priestifeld.
In total, the teams have faced off 17 times, and honours are even at six wins apiece. There have also been five draws.
How to watch
Fans cannot attend the game, but a match pass can be purchased for £10 to stream the game on iFollow.
Kick off is at 19:00 BST.
What the managers have said
He said: “We will pick a team that we think can win the game, that is the most important thing, and utilise the squad as we feel is appropriate.
“When you come off the back of a defeat as we had on Sunday, you want to try to correct that and there are opportunities to address things on Sunday which we were disappointed with.”
Gillingham manager Steve Evans maintained his lack of interest in the competition when speaking to the club website over the weekend.
He said: “We will make plenty of changes. I do not hide from the fact that Blackpool next Saturday is my priority.
“They have spent the most money this summer excluding Darragh MacAnthony at Peterborough United who, in fairness to him, always spends big money in search of success.”