L'Equipe says the midfielder has made a verbal transfer demand in recent days as he seeks to leave before the market shuts.
Several clubs from Spain, Italy and France are all in contact with Guendouzi's camp, though no names have been out forward.
The 21 year-old hasn't featured for Gunners manager Mikel Arteta so far this season.
Last week, Arteta said, "Matteo has been training like any other player in the squad. It is a new season and we had some really positive conversations between both parties, now he's back with the group, he is training really well, he went to France to play with the under-21s last week and played really well again, and he is here."
On speculation about Geundouzi being offered across European clubs, Arteta was coy.
He added: "I don't know, I am not going to discuss here what the things that happened internally. But a lot of the things they have been writing, I can tell you they are not true."