The Gunners are ready to approach the Juventus manager about succeeding Arsene Wenger at the Emirates Stadium, but will turn to ex-Chelsea boss Ancelotti if they are unable to reach a deal, according to the Daily Star.
The North London club are also said to have identified potential candidates to serves as the new appointment's assistant manager, with former Arsenal players Patrick Vieira and Mikel Arteta reportedly in the frame.
Bosnian coach Zeljko Buvac, who recently parted company with Liverpool, has also been linked with this role.
The report goes on to say that Arsenal originally approached Allegri last year when it was unclear whether Wenger would remain at the club for another season.
Allegri's wage demands could reportedly be set at £11m per year, after tax.