Wenger's future has been brought under intense scrutiny following the Gunners insipid performance in Sunday's 3-0 Carabao Cup final loss to Manchester City.
With the possibility of making the top-four looking increasingly unlikely, the Arsenal board are planning to review Wenger's contract.
The Frenchman signed a two-year extension at the beginning of this season.
But Starsport claim Ancelotti has told friends he wants to return to the Premier League with the north London club.
He won the 2009/10 Premier League title with the Blues before being fired at the end of the following season.
Other names being mentioned to replace Wenger include former Barcelona manager Luis Enrique, Germany national team manager Joachim Low, Celtic boss Brendan Rodgers and Manchester City assistant coach Mikel Arteta.