Mourinho made three major signings this summer in Victor Lindelof, Romelu Lukaku and Nemanja Matic - but missed out on adding the wide player he craved to his attacking armoury, failing to get a deal for Inter Milan's Ivan Perisic over the line.
Lemar didn't fancy a move to North London, with Liverpool believed to be his preferred destination.
And, according to the Mirror, the Portuguese chief has identified Lemar as the flawless player to fill the void.
The paper claims agents for the France worldwide have been made aware of Jose Mourinho's intentions to take the player to Old Trafford.
Alexis Sanchez to be used as makeweight in Thomas Lemar deal
Unfortunately for Gunners fans, Lemar did not join the list of big money players to move on from the Ligue 1 side in recent seasons and now, club vice-president Vadim Vasilyev has revealed why.
And Lemar is likely to be tempted by a Premier League challenge with United.
The Chilean striker's contract runs out at the end of this campaign and he is unlikely to sign an extension.
With that in mind, Monaco were evidently able to turn down a fee for Lemar that was more than double what they allowed Silva to go for earlier in the summer, even though the Portuguese winger is similarly influential and only little more than a year older.More news: Category 5 hurricane IRMA looms, updated forecast track just in