The 58-year-old, who is one of only two managers to have won the Champions League three times, is understood to want to stay in club management and is particularly keen on a return to the Premier League.
The Mirror reports that Ancelotti was offered the Italy job following the team's failure to qualify for this summer's World Cup in Russia, but has now decided to reject the approach.
Arsenal remain on the lookout for someone to fill the shoes of Wenger, who will bring an end to his 22-year reign at the club this summer.
Luis Enrique and Massimiliano Allegri are considered the frontrunners for the job, but Ancelotti boasts past Premier League experience having led Chelsea to the Premier League and FA Cup double in 2010.
Former Manchester City boss Roberto Mancini and Leicester City manager Claudio Ranieri are now the favourites to take over the vacant Italy post as the Azzurri look to rebuild ahead of the 2020 European Championships.