The World Cup winner, who is a free agent from July 1, came off with a calf problem early in Tuesday’s chastening 4-0 loss at Liverpool, which makes a top-four Premier League finish unlikely.
“With Paul, as it seems after the scan we did the day before yesterday, it is very unlikely he will play until the end of the season,” Rangnick said on Friday.
The France midfielder came through the youth set-up at United and returned from a successful stint with Juventus in 2016 for a then world-record fee.
Although Pogba has won the Europa League and League Cup in his second spell at United, he has largely been a disappointment, with his lacklustre displays and repeated links with other clubs serving to irritate fans.
The 29-year-old was booed off the pitch when he was substituted during the recent win against Norwich.
Asked if Pogba has played his final match for United, Rangnick said: “The doctor told me it will take four weeks minimum for him to recover and the last game is the end of May.
“I don’t think that it is very likely that he will be able to play again.”
Rangnick was speaking the day after United confirmed Ajax manager Erik ten Hag would become the permanent boss at Old Trafford at the end of the season.
“I knew that Erik was one of the candidates the board spoke to,” he said. “Obviously I told them, at least from what I have seen and known from people who had worked with Erik, that I think he would be a good choice.
“I still believe that he is a very good choice.”
United’s immediate focus is on their match against top-four rivals Arsenal on Saturday, with captain Harry Maguire set to line up in defence.
The England international had to report a bomb threat to police on Thursday and officers conducted a sweep of the home he shares with his fiancee and two young children.
“I haven’t seen him because I only got to know about this terrible, terrible thing yesterday afternoon,” said Rangnick. “Since then I haven’t been able to speak with him.
“But again this is another bad sign of the crazy world we’re living in.
“Obviously I feel very sorry for Harry that he had that terrible experience, but he knows that we’re all behind him — the club, everybody, the players, his team-mates.”