United conceded an injury-time equaliser in a 1-1 draw at a snowy White Hart Lane last weekend, allowing champions Manchester City to breathe new life into the title race by cutting their rivals' lead to five points.
United have gone nine years without winning the FA Cup, leading manager Alex Ferguson to state that he wants his side "to try and have a go" at it in the current campaign.
To that end, he will find little discouragement in Fulham's recent form.
Martin Jol's men, who squeezed past Blackpool after a third-round replay, have collected just 12 points from a possible 45 in the Premier League; a run that has seen them slide to 14th in the English top flight.
The United squad have spent the week in Qatar for a warm-weather training camp ahead of Saturday's reunion with former striker Dimitar Berbatov.
The Bulgarian is expected to make his first appearance at Old Trafford since leaving the club in the close season and United defender Phil Jones is looking forward to pitting himself against his former team-mate.
"It'll be great to see Berba back at Old Trafford. Technically he's a fantastic player," he said.
"The FA Cup is a great competition and one we want to win. We want to go as far as we can. It's a competition I've always admired.
"Hopefully we can get the result we want and continue to progress in the competition."
Arsenal, without a trophy of any description since beating United on penalties in the 2005 final, will hope to carry their mid-week momentum into the cup when they visit second-tier Brighton and Hove Albion.
Brighton knocked out Newcastle United in the third round, but Arsenal go into the game on the back of a 5-1 thrashing of West Ham United on Wednesday that reinvigorated their challenge for Champions League qualification.
"I never felt that the players didn't know how important it is," said Arsenal manager Arsene Wenger.
"I was more worried that they are a bit sometimes inhibited in the recent big games from the start. But this team has a fantastic mentality and good quality. That's what we want to show until the end of the season now."
As in the previous round, the draw for round four was low on all-Premier League confrontations, with Manchester City's trip to Stoke City the only other tie to feature two top-flight clubs.
Stoke were thrashed 4-0 by Chelsea in their last home game but they boast an excellent home record against City, who have not won at the Britannia Stadium on their last six visits.
Minnows in need of inspiration need look no further than Bradford City, who overcame Aston Villa in the League Cup semi-finals in mid-week to become the first English fourth-tier side to qualify for a major Wembley final.
Macclesfield Town of the fifth-division Conference National, conquerors of Championship leaders Cardiff City in round three, host Wigan Athletic, who needed a replay to see off third-tier Bournemouth in the previous round.
Fellow non-league side Luton Town, who slipped out of the Football League in 2009 after going into administration, also face top-flight opposition in the form of Norwich City.
Sunday offers up three evocative cup ties, with third-tier Brentford and Oldham Athletic gunning for upsets against the respective might of Chelsea and Liverpool, while Tottenham travel to Leeds United.
Chelsea will be eager to return to action after going out of the League Cup to Swansea City on Wednesday in a game that saw Eden Hazard sent off for kicking a ball boy.
Millwall v Aston Villa
Saturday (1500GMT unless otherwise stated):
Stoke City v Manchester City (1245GMT), Bolton Wanderers v Everton, Brighton and Hove Albion v Arsenal, Derby County v Blackburn, Huddersfield Town v Leicester City, Hull City v Barnsley, Macclesfield Town v Wigan Athletic, Middlesbrough V Aldershot Town, Norwich City v Luton Town, Queens Park Rangers v Milton Keynes Dons, Reading v Sheffield United, Manchester United v Fulham (1730GMT)
Brentford v Chelsea (1200GMT), Leeds United v Tottenham Hotspur (1400GMT), Oldham Athletic v Liverpool (1600GMT)