The Gunners are understood to have earmarked the Frenchman as a possible target when the transfer window reopens, with uncertainty continuing to surround the long-term future of captain Pierre-Emerick Aubameyang.
The Express reports that Arsenal boss Mikel Arteta is a big fan of Edouard, but that it will take a bid in excess of the £25m Arsenal paid Celtic for Kieran Tierney last summer to prise him away from the Scottish champions.
The 22-year-old's contract at Celtic does not expire until 2022, meaning that Neil Lennon's side have no immediate need to sell him and they remain hopeful that he could still sign a new deal.
Everton have also been linked with a move for the France Under-21 international, who has scored 27 goals and created 19 more across all competitions this season.
Across Europe's top five leagues only Lazio's Ciro Immobile has had a hand in more league goals this season, with Edouard netting 21 and assisting 12 in the Scottish Premiership.