The north London side have been fending off interest from Red Devils in the 27-year-old England left-back.
Tottenham sold England international Kyle Walker in a £52m deal to Premier League leaders Manchester City.
Rose spent most of the second half of the 2016-17 season on the bench due to a serious knee problem.
The England left-back has reportedly fallen out with Spurs manager Mauricio Pochettino over the past week.
Former Arsenal striker Wright believes Rose would give the Manchester United team an additional boost.
Wright told BBC Radio 5 Live: ”Man United could need some extra thrust in January. If Kyle has gone for £50m, then Rose has to be in and around that kind of money.”
Rose has established himself as one of the Premier League’s best left-backs over the past couple of seasons.
The Englishman was a key of the Tottenham team that finished in third place last term before a runners-up spot this term.
Manchester United signed Benfica defender Victor Lindelof, Chelsea midfielder Nemanja Matic and Everton striker Romelu Lukaku last term.
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