The Swans are flying high in the Championship and enter this game as strong favourites against a Stevenage side sitting 22nd in League Two.
This weekend's meeting will be the first time Stevenage have hosted Swansea since a Football League Trophy match in October 2002.
A lot has changed since then, particularly in the case of Swansea, who have spent seven seasons in the Premier League.
The Swans are now aiming to return to the top flight following relegation in 2018 and they are looking good value to achieve exactly that.
Steve Cooper's men beat Watford 2-1 last weekend and are in the automatic promotion zone with 23 games of the Championship season played.
City are unbeaten in four league outings, winning three of those, but focus now switches to a possible cup run in a competition that they have never previously won.
Stevenage would also love a run deep in the competition, but their main target this campaign is surviving the drop in League Two.
Former Cardiff City player Alex Revell is the man in charge at the Lamex Stadium and has seen his side hit form at just the right time.
The hosts have won back-to-back matches - 1-0 against Cambridge United and 3-1 against Scunthorpe United - to climb out of the dropzone on goal difference.
They will look to carry that form into the FA Cup as they look to build on an impressive return of four wins from six third-round ties.
This is Swansea's first FA Cup match against League Two opposition since February 2018, meanwhile, when winning 8-1 against Notts County in a fourth-round replay.
Stevenage form (all competitions): DDLDWW
Swansea City form (all competitions): WLWWDW
Brandon Cooper is another who will play no part, having already featured in the competition for Newport County this season.
As for Stevenage, boss Revell has indicated that he will field a strong lineup in the hope of pulling off an upset, a decade on from his club's famous win over Newcastle United.
Stevenage possible starting lineup:
Cumming; Hutton, Vancooten, Cuthbert, Coker; Aitchison, Smith, Read, Pett; Carter, Newton
Swansea City possible starting lineup:
Benda; Naughton, Cabango, Guehi, Manning; Fulton, Grimes; Garrick, Dhanda, Routledge; Cullen
We say: Stevenage 1-3 Swansea City
Swansea's main focus this season will be on earning promotion to the Premier League, but this favourable third-round tie presents Cooper's men with a chance to keep their momentum going.
Stevenage are at risk of dropping out of the Football League, though they have won back-to-back matches and an upset cannot be completely ruled out this weekend.