Forward Marcus Rashford will miss United's penultimate game of the campaign with bronchitis, while central defender Eric Bailly may be unavailable with a back issue.
Left-back Luke Shaw, winger Jadon Sancho and central midfielder Paul Pogba will also not feature for the Reds in the 5.30pm clash at the Amex.
Shaw had metal bolts removed from his leg in April and Rangnick said he didn't think the 26-year-old would feature again this season.
Pogba, meanwhile, is out indefinitely with a calf injury and Sancho is expected to be sidelined with tonsillitis.
But, in better injury news for the Reds, captain Harry Maguire has recovered from his knee injury and veteran striker Edinson Cavani is back in full training.
Speaking to the Manchester Evening News, Rangnick said: "Harry is back in training. He trained the whole week since the second day after the Brentford game, so he will be available for tomorrow and part of the group.
"Edinson is in training, obviously, he came on as a substitute [against Brentford on Monday].
"Marcus Rashford will be missing, he has got bronchitis with a high temperature, so he won't be able to be part of the group and we have a question mark behind Eric Bailly, he called the doctor this morning and had some back problems and he is being checked right now.
"We will have to see if he will be able to train afterwards."
Speaking on whether Maguire will start at the Amex, Rangnick added: "This is a decision I have to make after training today and obviously, I don't want to tell our opponents with which line-up we are going to start but he will definitely be part of the group."
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