Neil Harris' side face a fight to preserve their place in the second tier of English football but did end a four-match losing streak with a 2-0 win at Birmingham City on Wednesday.
However, the Championship outfit - the lowest ranked team left in the competition - are unbeaten in their last nine home matches in the cup, including victories against Watford, Leicester City and Everton.
Nevertheless, it is Brighton who are favourites to secure a semi-final spot. The Seagulls can be backed at 23/20 (2.15) to win this one inside 90 minutes. William Hill offer just 8/15 (1.53) that the Premier League side qualify for the final four.
Millwall are a 5/2 (3.50) shot to win in normal time, while Harris' men are available at 11/8 (2.38) to progress. William Hill go 11/5 (3.20) that Sunday's showdown remains deadlocked at the end of 90 minutes.
Harris has admitted that avoiding relegation is his primary priority for the Lions. Nevertheless, the Millwall boss is expected to name his strongest possible side.
Yves Bissouma is suspended, while Mathew Ryan is likely to be rested with David Button set to deputise. Pascal Gross and Florin Andone will both be assessed, while Jose Izquierdo could make his first start since December.
Millwall have won eight of their last nine FA Cup ties on their own patch. Furthermore, Harris' men have collected 24 of their 37 league points so far this season at home and are available at just 4/6 (1.67) to avoid defeat inside 90 minutes.
There have been at least three goals scored in each of Millwall's last four FA Cup ties on home soil and the Lions have found the net in each of their last 12 home matches in this competition.
William Hill offer 6/5 (2.20) that there are more than two goals scored in this game or 10/11 (1.91) that both teams are on target. The hosts can be backed at 12/5 (3.40) to score more than one goal against Brighton.
Brighton's big chance
Remarkably, the Seagulls have not made the final four of this competition since finishing up as runners up to Manchester United in 1983. Brighton lost at this stage of the competition last term, but Hughton's men will have high hopes of a trip to Wembley.
With the Lions perhaps more focused on securing their place in the Championship, Brighton look well-placed to take advantage. William Hill's 23/20 (2.15) quote, then, for the Seagulls to win on Sunday could offer outstanding value for punters.