Lemar has also reportedly agreed terms with the Gunners, with the 21-year-old set to sign a five-year deal worth £250,000 per week.
The apparent agreement does not depend on Alexis Sanchez leaving in the winter window, with his contract due to expire in summer 2018.
Gunners boss, Arsene Wenger, last week hinted that he would go back for the France winger, after failing to land him on deadline day for £92million.
“He decided to stay at Monaco,” Wenger told Telefoot.
“Did we make a €100m offer? Yes. Are we going to make another offer? Yes.
“He is always ready to receive the ball, he is quite complete in both defence and attack.”