Simone Inazghi and Roberto Donadoni have been linked with the Lazio bench, but it seems that a new candidate has emerged.
It was a disappointing season for Lazio, who missed out on Europa League qualification, finishing in ninth place.
The Biancocelesti struggled a little with the loss of star midfielder Hernanes, who was sold to Inter in January, and inconsistency cost the Eternal City side.
Veteran coach Edy Reja isn't expected to stay on for next season and if he does it may well be in a directorial role.
Allegri made his name at Cagliari having impressed at Sassuolo and he earned the call to the prestigious Milan bench in 2010.
While Allegri delivered the title in 2010-11, things steadily went downhill and he was sacked midway through last season with the Rossoneri languishing.
La Gazzetta dello Sport believes that Lazio have already made contact with Allegri and that sporting director Igli Tare is ready to discuss terms with him.
Allegri reportedly wants a three-year deal worth around £2m per season plus assurances that star players Antonio Candreva and Senad Lulić won't be sold, as well as the arrival of Davide Astori.