Wenger is entering his last week as Gunners boss and the club’s hierarchy have already begun the process of appointing his successor.
According to the UK Independent, Arsenal are conscious of the need for a manager who “galvanises” the fanbase.
Even though some at the club feel they should do what they did with Wenger in 1996 and opt for a promising but lesser known name, there is a feeling the new man must excite the supporters.
Allegri has won three Italian titles in a row and is on the brink of a fourth, but has also taken Juve to two Champions League finals.
Negotiating with the Serie A champions could be tricky, however, although Allegri is said to be considering another challenge and is interested in the job.