Wenger, who still had a year remaining on his contract, has decided to call time on his 22-year stint at Arsenal at the end of the season.
The 68-year-old announced his decision to Arsenals players and staff on before the news was made public on Friday morning.
Ancelotti, who is one of the frontrunners to replace Wenger, has been out of work since he was sacked by Bayern Munich at the end of September.
The Italian already has Premier League experience having won the league and cup double in his first season at Chelsea, while he also guided Real Madrid to their historic 10th Champions League trophy in 2014.
Reports in Italy have suggested that Ancelotti is holding out for the Arsenal job and favours a move back to the Premier League.
Arsenals CEO Ivan Gazidis claimed on Friday that the club have yet to approach candidates to succeed Wenger, but Ancelotti has indicated that he wants another managerial job.
The future of the manager doesnt depend on the manager, Ancelotti said at a press conference in Geneva on Friday.
I can say I would like to work again, but it doesnt depend on me.
If I find the right possibility, the right project, I would be delighted to continue.
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