The France international, 21, is seen as a direct replacement for Alexis Sanchez.
Should the Gunners land Lemar, Sanchez will be allowed to leave for Manchester City.
City have today offered £55m plus £5m in add ons in a second move for Sanchez.
Liverpool have pursued Lemar too and bid £74m for him but Arsenal now lead the hunt ahead of tonight's 11pm transfer deadline.
Arsenal will now await the answer to their £90m bid, according to the Daily Mail.
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