Anthony Martial has been ruled out of Manchester United's Champions League tie with Young Boys and the weekend trip to Norwich City.
The striker hurt his knee in training before the 1-0 victory over Crystal Palace on Sunday and will be frustrated at being unable to impress the new boss.
Although the injury is not thought to be too serious, it means he is joining fellow Frenchman Paul Pogba on the sidelines.
“Anthony trained with us on Saturday in the final session before the Crystal Palace game,”
revealed Rangnick during his press conference. “Half an hour after training, the doctor and the medical department informed me he has some pain on his knee.
”We had a meeting together with the doctor, the medical department and Anthony and we agreed he should try to recover from that. It's not a fresh injury, it's symptoms he had in the past already.
“We need to make sure he is reducing the amount of pain in the next couple of days and, hopefully, have him back next week.”
Raphael Varane and Edinson Cavani are also being treated carefully and look set to resume full training next Monday, even though they were spotted with the group at Carrington on Tuesday morning.
“Edi did [train] yesterday but it was the first time Raphael was on the pitch together with the team,”
explained Rangnick. “If everything goes well, I expect both of them back in full training next week, hopefully Monday next week, they will be participating in all training sessions. Obviously, they're both top players, we would be happy to have them on board as soon as possible but, especially with Rapha and his injury record in the past, we need to make sure that we will have him at the end of the season.
"So it's also about sustainability and not only getting him fit as soon as possible. It would be great to have both players available as soon as possible but, as I said, if possible, for the rest of the season.“