That’s according to Sky Bet who reckon the Red Devils have edged ahead of Arsenal in the race for the winger.
A move to United is now priced at 13/8 before the transfer window shuts.
Meanwhile Arsenal are second favourites at 3/1 to secure his signature.
The Gunners have been repeatedly linked with the France international as Arsene Wenger looks to bolster his ranks.
However, a deal has failed to materialise.
United have also been widely expected to draft in another wide man.
“Thomas Lemar is wanted by Arsenal and Man Utd”
Inter Milan ace Ivan Perisic has been touted as a potential arrival.
But United have been similarly frustrated in their attempts to bring in fresh wide options.
Lemar was a standout performer for Monaco last term as they stormed to Ligue 1 glory.
The 21-year-old, who can also played in a central midfielder role, has racked up 62 appearances for the club since signing from Caen in 2015.
Monaco have sold a string of last season’s heroes including Tiemoue Bakayoko, Bernardo Silva and Benjamin Mendy.
Vice-president Vadim Vasilyev insisted last month that Lemar would not be joining the departures list.
He said: “We have kept all of the key players that we intended to keep.
“And I will address speculation relating to Lemar – he is staying with us. He is an immense talent and is essential for the team.”