The Rossoneri are trying to offload the striker who cost €12 million in 2013.
According to Sky Sport Italia the forward could be closing to signing for Lazio.
Matri spent last season on loan at Genoa where he impressed scoring seven goals.
But his loan spell was cut short and he joined Juventus on loan in January.
Lazio only have Miroslav Klose and Filip Djordjevic as striking options.
Olympique Marseille are also keen on signing the 31 year-old poacher.
However, negotiations are already ongoing between Milan and Lazio.
