The 30-year-old spent last season on loan at Genoa and Juventus, respectively, helping the latter to Coppa Italia glory by netting the winner in the final against Lazio.
Matri is now back with the Rossoneri, though, and is determined to make an impact at San Siro.
"I want to stay at Milan and do really well here," Matri told La Gazzetta dello Sport.
"My objectives for 2015-16 are to stay at Milan, score a lot of goals, play well and help Milan back into the Champions League.
"I hope to be useful to this team. I will talk with the coach and the club."
Matri came through the ranks of the Milan youth academy, but left the club at a young age failing to secure regular first team action.
He then returned to his boyhood club in 2013, only to leave again shortly after. The forward is determined to do better this time around, though.
"I have a huge desire to do well at Milan now, but feel less pressure than before. I have found my confidence again.
"I wanted too much on my first return to Milan. I did not feel ready and was criticised right from the start."