Lemar scored twice for France in their 4-0 thrashing of Holland in a 2018 World Cup qualifier on Thursday night.
The Gunners offered £90million for Lemar earlier in the day, but called off the deal with little time left to complete it. That also ended Alexis Sanchez’s hopes of moving to Manchester City.
After his starring performance at Paris’s Parc des Princes, Lemar was cryptic when asked about a potential move.
“You will soon see for yourself, but for the moment I am a Monégasque and everything is going very well,” he said on TF1.
Monaco were also unwilling to let the 21-year-old leave, after most of their stars left this summer.