The Norfolk club have not recorded a victory over the Craven Cottage outfit since March 1986, a 2-1 league success.
The two sides have met on 13 occasions in all competitions since then, with Fulham winning 10 of those encounters.
The last of those Fulham victories came on Boxing Day when Rene Meulensteen's men recorded a crucial three points in their fight against Premier League relegation as strikes from Pajtim Kasami and Scott Parker wiped out Gary Hooper's opener.
Meulensteen's side head into Saturday's showdown at Carrow Road on the back of a morale-boosting 2-1 victory over fellow strugglers West Ham on New Year's Day.
After falling behind to Mohamed Diame's strike, the hosts bounced back courtesy of goals from Steve Sidwell and Dimitar Berbatov as Fulham showed great spirit in response to the humiliating 6-0 defeat at Hull City last weekend.
Fulham's best FA Cup run came when the London club reached the 1975 final, where they lost 2-0 to West Ham, while they have failed to progress past the fourth round in the past two seasons, with a 4-1 loss to Manchester United ending their hopes last year.
Norwich's recent history in the competition has not been favourable. City have failed to go beyond the fifth round since losing 1-0 to Sunderland at the semi-final stage in 1992 and suffered a shock 1-0 defeat to non-league Luton Town in round four in 2013.
Chris Hughton's men have endured a blip in the last month and have failed to record a victory in their last five matches, drawing three and losing twice.
A 1-1 draw at Crystal Palace on Wednesday saw Jason Puncheon's penalty cancel out Bradley Johnson's opener.
Norwich will be without midfielder Leroy Fer as he serves a one-match suspension after receiving two yellow cards against Palace, while there are fitness doubts over centre-back Michael Turner (hamstring) and midfielder Jonny Howson (back).
Fulham have no fresh injury worries with goalkeeper Maarten Stekelenburg (ankle) and defender Brede Hangeland (leg) set to miss out.
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