Milan's defeat at home to Manchester United, the first in their history, left club patron Silvio Berlusconi furious, says Gazzetta dello Sport.
The Italy PM has concerns over Leonardo's tactical nous and is considering dumping the Brazilian.
The two names that top his shortlist are free agent Marco van Basten and Allegri.
Allegri has also been linked with Juventus and Fiorentina. However, Milan's sound relationship with Cagliari president Massimo Cellino has them favourites should they decide to move for the experienced coach.