The Bees have reached the fifth round stage for the first time since 2006 and are looking to reach the quarter-final stage for the first time since 1989.
Safe of the relegation zone (for now) and adrift of the playoff race, Brentford fans will be eager for this cup run to extend past this weekend.
Swansea’s top scorer Oli McBurnie is in line to start in Sunday’s FA Cup fifth-round clash with Brentford after struggling with illness.
McBurnie has scored 16 goals so far this season but has made limited appearances in recent weeks due to flu, although could return to the starting line-up this weekend.
Swansea manager Graham Potter wants his side to focus on fellow Sky Bet Championship opponents Brentford and not the potential perks of an extended cup run.
Swansea has won their last five meetings with Brentford in all competitions, including a 3-2 win in December in the Championship.
The only previous FA Cup meeting between Swansea and Brentford was in the first round in 1971-72, the Swans winning 3-2 after a replay.
Swansea are looking to reach the FA Cup quarter-finals in consecutive seasons for the first time since the 1925-26/1926-27 campaigns.
Team News of Swansea City vs Brentford
Defender Henrik Dalsgaard could be in contention despite breaking a bone in his hand in training this week while Rico Henry is still to be assessed after a recent foot problem.
Swansea winger Nathan Dyer is a doubt with a hamstring problem, while Leroy Fer (hamstring), Declan John (ankle) and Wayne Routledge (calf) are all out. Joe Rodon (foot) and Martin Olsson (Achilles) remain longer-term absentees.
Brentford will assess Rico Henry, who has been sidelined with a foot injury. Henrik Dalsgaard is hoping to play, despite breaking a bone in his hand in training last Monday.
Swansea’s Oli McBurnie could start after returning from illness to come on as a substitute in midweek.
Nathan Dyer is a doubt with a hamstring problem, while Leroy Fer, Declan John and Wayne Routledge are all ruled out with hamstring, ankle and calf injuries respectively.
Brentford will assess Rico Henry, who has been sidelined with a foot injury.
Fellow defender Henrik Dalsgaard is hoping to play, despite breaking a bone in his hand in training last Monday.
Score prediction: Swansea 1-0 Brentford
TV channel and live stream, and online coverage
The match will be televised live on BBC One Wales.
You can also follow all the action with NewGersy Sport’s LIVE blog.
YOU CAN FOLLOW MATCH HERE
There have been 82 meetings between these sides over the years with Swansea just edging things with 31 wins to Brentford’s 29.