Arsenal are set to make another move for the 21-year-old, after missing out on the forward on transfer deadline day - with Alexis Sanchez missing out on a move to Manchester City as a result - but this time they will face serious competition from United, according to the Mirror.
The same article states that Arsenal are prepared to offer the promising France worldwide a five-year contract worth in the region of £250,000 a week.
Arsenal also have maintained an interest in signing Manchester City's winger Raheem Sterling.
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Lemar's brimming potential, youthful exuberance and versatility to play in any attacking position is undoubtedly something that Arsenal could benefit from, especially after Alex Oxlade-Chamberlain's departure to Liverpool.
Arsene Wenger has said any bid for Lemar does not rest on Sanchez being sold though the Chilean, who is in the final year of his contract with the Gunners is likely to again be pursued in January. But, filling Sanchez's shoes will be a tall ask for the youngster.
And, according to the Mirror, the Portuguese chief has identified Lemar as the ideal player to fill the void.
By the looks of it, Arsenal will probably be most desperate to sign Thomas Lemar, but where the player ends up remains to be seen.