The sides drew 1-1 in the original fixture and must do it all again with a fourth round trip to League One Sheffield United the prize for the winners
The two battled to a 1-1 draw in their original third-round tie earlier this month as Robert Snodgrass cancelled out Darren Bent's opener to set up a replay that both managers could arguably do without.
With top-flight survival still the main priority, just a point separates Norwich, who are 15th, and Fulham in the league as the duo linger ominously just above the relegation zone.
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A fourth-round trip to Sheffield United - who dumped Aston Villa out to progress - awaits the winners and both sets of players would welcome a morale-boosting victory on Tuesday to build momentum and belief.
Recent encounters with Norwich should offer Fulham some cause for optimism, with confidence likely to be in short supply following Saturday's 4-1 home loss to fellow strugglers Sunderland.
Fulham boast an impressive 14-match unbeaten record in all competitions against the Norfolk club, a run that stretches all the way back to March 1986, including a 2-1 Boxing Day victory at Carrow Road earlier in the season.
Head coach Rene Meulensteen will be desperate for a positive response to the Sunderland loss, and his side have now conceded 46 goals in the Premier League in 2013-14, more than any other top-flight team.
"We keep working on it and it needs to improve, it’s as simple as that," the Dutchman told reporters.
"In general, the performances have improved. But the quality into the final third and conceding is a problem."
Meulensteen could be boosted by the return of Brede Hangeland to the centre of defence after a three-month lay-off with a back injury.
Goalkeeper Maarten Stekelenburg is likely to miss out with a foot injury, while Matthew Briggs is also sidelined with a groin problem.
Norwich, who crashed out to non-league Luton Town in the fourth round of this competition last year, are winless in their last seven games following a 2-0 defeat at Everton on Saturday, with the side's last victory a 2-0 success at West Brom at the start of December.
Manager Chris Hughton still has a number of injury concerns ahead of the trip to London, with Jonny Howson (back), Alex Tettey (ankle) and Anthony Pilkington (hamstring) all unlikely to feature, while Elliott Bennett (knee) and Michael Turner (hamstring) are both ruled out.