Cavani has recently been unavailable for selection due to a tendon issue, while Varane has been out since suffering a hamstring problem while representing France last month.
Rangnick has ruled the pair out of Wednesday's Champions League clash with Young Boys and Saturday's Premier League contest with Norwich City, but the German said that both are due to resume "full training" next week.
"They were part of the training session today and, 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," Rangnick told reporters ahead of Wednesday's match against Young Boys at Old Trafford.
"They're both top players. Of course 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 until the end of the season, so it is 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 obviously for the rest of the season."
Summer arrival Varane has only made nine appearances for the 20-time English champions this season, having also picked up a groin injury in October.
Cavani, meanwhile, has been restricted to just eight outings in all competitions, with his only goal of the campaign coming away to Tottenham Hotspur at the end of October. body check tags ::