Fulham may be 47 places above United in the league ladder, but some bookmakers regard the Barclays Premier League side as underdogs for this weekend's clash at Bramall Lane.
Fulham's form has improved since Meulensteen took over from Martin Jol, but the Londoners still sit just one point above the drop zone and they have a game against fellow relegation candidates Swansea on Tuesday night.
With just 51 hours separating the two games, Meulensteen has no option but to save his top players for the clash against Swansea, who are two points above them in the league.
"The Swansea game is more important because it is so tight in the Premier League," Meulensteen said.
"There is not one country in the world that would let someone play in a fourth round of the cup on a Sunday and then play an important league game on Tuesday.
"Everyone with a bit of common sense understands that.
"I have to utilise the squad to the best of my ability, to make sure it doesn't affect either competition."
Meulensteen said it was a "possibility" that he could field two completely different teams for the games against United and Swansea.
To further complicate matters for Meulensteen, Fulham face Southampton four days after their trip to Wales.
Still, having spent 11 years working in various roles at Manchester United, Meulensteen is well versed in the importance of cup competitions.
A good cup run can often prove problematic for relegation candidates, though, as Wigan and Birmingham have found out in recent times, but Meulensteen is not concerned that progress would hinder his ability to keep Fulham in the top flight.
"There are some examples with previous clubs who have gone down," the 49-year-old said.
"But that is a negative way of thinking, it's almost like coming up with an excuse.
"That is not the way you can look at it. You need to make sure that you respect both competitions.
"It can provide you with a boost and I am 100 per cent sure that the people of Birmingham and Wigan, who went to that beautiful day at Wembley and came out winners, they will always remember that.
"It's part of their history. That is a massive thing for those people.
"They have paid a heavy price dropping out of the Premier League, but they will always be remembered as cup winners."
The good news for Meulensteen is that he has almost an entire squad to choose from for the game at the Sky Bet League One side.
The only injury doubt for the Cottagers is defender Fernando Amorebieta, who has a knee problem.
Among the squad players who could feature are Elsad Zverotic, Lasse Vigen Christensen and Aaron Hughes.