The offer will, however, be much less than the £90m they offered on transfer deadline day this summer.
Arsenal will not return with such an inflated figure as their bid was bolstered by the £60m that Manchester City were willing to pay for wantaway star Alexis Sanchez in August, but that move also fell through.
Since the start of the 2017/18 campaign, Lemar has failed to find the scintillating form that put his name on the map but, crucially, he is understood to be open to the idea of leaving Monaco.
The French club are also very aware that the 22-year-old, who has two and a half years left of his current deal, is now unlikely to to attract more than what was offered in the summer again and could therefore sell at the next opportunity.
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