The Rossoneri's budget may mean that the Juventus striker could be targeted to replace the free-scoring Swede after his move to Paris Saint-Germain on Wednesday
The Rossoneri's CEO stated on Wednesday that the San Siro side will replace the Swedish star - whose 28 goals saw him top the scoring charts in Italy last term - with a "champion".
Matri would fit the bill in a literal sense, having collected a Serie A winner's medal last term, but spent chunks of the past campaign on the bench.
However, the publication understands that Galliani regards high-profile names in Europe, such as Manchester City's Edin Dzeko and Carlos Tevez, as too expensive, and is instead looking at the more affordable Matri.
Although the 27-year-old has not always been a starter for the Bianconeri, he still scored 10 goals in 31 appearances in 2011-12 after securing an €18 million transfer from Cagliari last summer following a successful loan spell.
One other option Massimiliano Allegri's side are believed to be considering is Brazilian striker Leandro Damiao, whose agent was reportedly in Milan on Wednesday.
The striker has earned nine caps for Brazil and will be in the shop window this summer, as he is set to play for his country at the Olympics.