The Gunners have been chasing Lemar all summer but are not thought to be close to striking a deal.
Monaco want big money for the Frenchman, and Man Utd have reportedly now joined the Gunners in the chase for his signature, with a £55m fee mooted for the 21-year-old.
It was claimed yesterday Jose Mourinho has turned to the French midfielder as he looks to make a fourth signing before the end of the transfer window on August 31.
And United fans are excited by the prospect of snapping up the Monaco star - and getting one over on London giants Arsenal in the process.
“Arsenal fans must be bricking it right now,” one fan teased on forum Red Cafe.
Another supporter added: “I don't see this happening, but I would love it just for the Arsenal fans reaction.”
A third posted: “He's a weird one for me. I don't really want us to sign him as I don't see how he'll fit in without drastically reducing Martial and Rashford's minutes.
“But I also don't want Arsenal to sign him.”
An Arsenal fan said letting Lemar slip through their fingers would be the final straw.
He posted on Twitter: “If Manchester United sign Thomas Lemar, I'm not watching an Arsenal match until Wenger leaves.”
Both Arsenal and Man Utd have until 11pm on August 31 to seal a deal for Lemar before the transfer window closes.
Scouts from the two clubs have a chance to see him in action against tonight, when Monaco take on Marseille in the French top flight.