The Swans beat Stevenage 2-0 to progress to this stage, while Forest - 21 points worse off than their opponents in the league - eliminated Cardiff City with a 1-0 victory.
The winners of this tie will face either Cheltenham Town or Manchester City for a place in the quarter-finals.
Swansea are flying high in the Championship after stringing together a five-game unbeaten streak, winning four of those matches to move into second place.
The Swans' midweek trip to Blackburn Rovers was called off due to a waterlogged pitch, meaning that they have had a full week's rest heading into this cup tie.
Forest, by comparison, were in action against Middlesbrough on Wednesday, going down 2-1 at the City Ground to remain in real relegation danger.
The Reds are five points clear of the dropzone, but they have played three games more than Rotherham United in 22nd place.
That loss to Boro ended Forest's seven-game unbeaten streak in all competitions, a run that includes a victory over Cardiff in round three of the FA Cup - Lyle Taylor's early goal proving the difference in that tie.
Chris Hughton's men will now be looking to do likewise against another Welsh side in Swansea, with this just the second ever meeting between the clubs in the FA Cup - the other ending in a 2-1 win for City in 1929.
The most recent encounter between the sides ended in a 1-0 win for Swansea at the end of November, but the Swans have not won back-to-back games against Forest in all competitions since 1953.
Swansea have a good home record in this competition, too, having won five of their last seven at the Liberty Stadium, albeit their most recent FA Cup match there ended in a narrow defeat to Man City, whom they may face again in round five.
That will also be the aim for Forest, of course, as they look to advance past this stage for only the second time in 16 campaigns, most recently doing so in 2013-14.
Swansea City FA Cup form: W
Swansea City form (all competitions): WWDWWW
Nottingham Forest FA Cup form: W
Nottingham Forest form (all competitions): DDWWWL
The midfielder may slot straight into the starting lineup on Saturday, most likely alongside Matt Grimes.
Swansea have a big game against Brentford to come in the league four days after this cup tie, but Steve Cooper's men have had a week off so a fairly strong XI can be expected here.
As for Forest, they will be without Yuri Ribeiro after the left-back was sent off against Middlesbrough on Wednesday.
Striker Taylor has scored seven goals in his last five FA Cup appearances, netting the winner for Forest in the last round against Cardiff.
Swansea City possible starting lineup:
Woodman; Naughton, Cabango, Guehi; Garrick, Hourihane, Dhanda, Grimes, Manning; Gyokeres, Routledge
Nottingham Forest possible starting lineup:
Smith; Jenkinson, Worrall, McKenna, Bong; Arter, Cafu; Lolley, Guerrero, Ameobi; Taylor
We say: Swansea City 3-1 Nottingham Forest
Swansea have been far superior to Forest in the Championship this season and beat the Reds when they last met in November.
The Welsh side have also had some extra rest heading into this fourth-round tie, all of which points towards a home victory on Saturday.