The Gunners' current boss, who has been at the helm of the North London club for more than two decades, does not come to the end of his contract until 2019.
Despite pressure from fans to resign last season, Wenger ended up signing a two-year contract, but according to the London Evening Standard, Ancelotti could be waiting in the wings if the Frenchman decides to leave early.
Any decision on Wenger's future is likely to be made when the season comes to an end, which will allow the coach to assess the campaign.
As it stands, Arsenal have two realistic chances of winning silverware as they remain in the Europa League and EFL Cup, but they will have to settle for a top-four battle rather than a race for the title as they sit sixth in the standings, 23 points behind leaders Manchester City and five adrift of fourth-placed Liverpool.
Ancelotti has been out of work since getting sacked by Bayern in September last year.