The Italy international is on a season-long loan deal at the San Siro, but has scored just three times in 17 appearances for Milan.
And Galliani believes the 25-year-old has much to do in the remainder of the campaign to convince Milan to make his deal permanent.
Galliani said: "We really like Mario, but he has to convince us to earn a permanent deal.
"Mario is feeling well. He is desperate to stay here at Milan. But like I have said before, he does not merit a permanent deal at the moment."