Defender Marcos Rojo is also facing a lengthy layoff with knee ligament damage.
Daley Blind replaced Rojo in the first half and Mourinho said that the Netherlands defender was a suitable deputy if the Argentina global were to miss extended time, while adding that Phil Jones and Chris Smalling are nearing returns from injuries of their own.
Manchester United defeated Anderlecht in the Europa League quarterfinals by winning 3-2 on aggregate.
"We are in trouble".
Wayne Rooney could be thrown into action sooner than planned by Manchester United to solve a growing injury crisis that has left manager Jose Mourinho to warn: "We're in trouble".
United now sits fifth in the EPL table, four points adrift of Manchester City in fourth for the final Champions League place and six behind Liverpool in third.
"But even with a insane mentality, they can not play Sunday. Now we need absolutely everyone", he added.
Mourinho's side have games against Manchester City, Arsenal and Tottenham Hotspur coming up as they attempt to qualify for the Champions League.
Zlatan was poor on the night but has been sensational for Manchester United and this injury could well play a big role in where the super Swedish striker plays his football next season.
Juan Mata, with just six goals, is United's next-highest league scorer. Nicky Butt could play him in that game because of his age. "After 90 minutes, before I knew that I have to change Zlatan, I had Ashley Young ready to come on and (Luke) told me, 'I am going to play this 30 minutes with cramps". "He could by age, so when you reach a certain level, and you reach that level for a long time, I don't think it makes sense, but the power is in their hands".
"These are the kind of things that make me trust players", he said.