The two clubs have trodden very different paths since they last met in the Barclays Premier League on January 30, 2007.
Fulham have contested a European final, slaying Italian giants Juventus en route to Hamburg in 2010 - the year after they claimed a record high finish of seventh in the top flight.
Although Fulham are fighting against relegation this season, they are in nowhere near as bad a shape as the club they will come up against on Sunday.
United, four-time winners of the FA Cup, were one of the founder members of the Premier League, but a second relegation from the top flight in 2007 triggered a downward spiral that has taken the South Yorkshire club to the third tier of English football.
The field once graced by Tony Currie, Gil Reece and more contemporary icons like Brian Deane now plays host to a team on the verge of the League One relegation zone.
Meulensteen knows his team must not take the Blades lightly, however.
"I warned the players they can't be complacent. I said that to them straight away (after the draw)," the Fulham head coach said.
"This will be a very difficult game. Sheffield United will try to chase everything and the crowd will get behind them.
"The key for us is to make sure we remain calm and focused and play away from that sort of pressure they throw at you.
"If you can maintain that, then the quality should see you through. But if you don't match their fighting spirit and enthusiasm you could be in for a tough, tough ride."
The Blades have climbed out of the relegation zone since Nigel Clough replaced David Weir as manager, but they are just one point above the bottom four having won one of their last six league games.
They delivered the shock of the third round when they dumped Aston Villa out of the cup three weeks ago, though, and Meulensteen admits the difference between the Blades' form in the two competitions is stark.
"It is like chalk and cheese. They are two completely different teams," the 49-year-old said.
"You think you are looking at completely different players in the Villa game, but that is what motivation and the challenge does, so we are prepared for a difficult game."
Although they sit 47 places below Fulham in the league ladder, United are favourites with some bookmakers to win Sunday's clash.
One of the main reasons behind this is because Meulensteen has admitted he will have to rest some of his first-team stars as Fulham take on fellow relegation candidates Swansea in the league on Tuesday.
One player who looks set to retain his place in the starting XI is 21-year-old defender Dan Burn.
After impressive loan spells at Yeovil and Birmingham, Meulensteen recalled Burn and threw him into the first team for the two third-round games against Norwich.
Meulensteen, who has vowed to bring through more players from Fulham's successful academy, was so impressed by what he saw that he then started Burn against Arsenal last week.
"I had no hesitation about playing him against Arsenal," the Fulham boss said.
"I got bags of confidence from his two performances against Norwich and from what he was doing in training.
"He acquitted himself really well."
Source : PA