Pogba has not played for United since Nov. 2 after picking up a thigh injury while on international duty with France. In December, Rangnick told Pogba to cut short his rehabilitation in Dubai and report back to Carrington for the rest of his recovery. The Frenchman is back in Manchester but his return to action is not imminent.
“A week ago I was told it would take another four or five weeks,” Rangnick told a news conference on Friday.
“I’ve seen him this morning before the training session but currently I don’t know how long it will take.
“He’s not training with the team yet. As far as I know from the medical department, it will last another three weeks, four weeks and once he is then fit for training it does not necessarily mean he is also match fit.
“It will probably take a couple of weeks before he is really able to compete for the first team.”
Pogba is facing a race against time to build up his fitness ahead of United Champions League round-of-16 first-leg clash with Atletico Madrid on Feb. 23.
The midfielder is out of contract at Old Trafford at the end of the season and if fresh terms are not agreed he will be able leave on a free transfer in June.