A source close to the club has told Reuters that Fletcher's former team mate Ole Gunnar Solskjaer and the club's ex-assistant coach Mike Phelan were set to return to Old Trafford as caretaker managers until the end of the season.
"Manchester United should never be in this position," Fletcher, who won who won five Premier League titles in 12 years at United, told the BBC.
"They're almost writing off this season and next season because if they appoint a new manager in the summer he's not going to have much time to look for new players."
Tottenham Hotspur boss Mauricio Pochettino has emerged as the bookmakers' favourite as United look for their fourth full-time manager since 2013 when Alex Ferguson retired after nearly 27 years in charge.
"There is a real concern that you could have two seasons of rebuilding again," Fletcher added.
United are sixth in the league, 19 points behind leaders Liverpool and 11 points off the Champions League places.
(Reporting by Hardik Vyas in Bengaluru; Editing by Peter Rutherford)
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