The Daily Mail says Vieira is one of the leading candidates to take over at the Emirates.
He is currently in charge of New York City in the MLS - but he also has an agreement with the American club that if there was an offer from a top European club that he wants to accept, he will be allowed to go.
Arsenal will be given all-clear to speak to Patrick Vieira if they want him to take over as boss
Vieira has already stated publicly that he is 'flattered' by the link with Arsenal and that he is ready to move back to European football.
He had two years running the Development squad at Manchester City and now has managerial experience at first team level.