The Uruguayan has so far failed to live up to his billing since a £12 million move from Bologna in the summer, but a return to Serie A does not look likely this January
Saints signed Uruguay international Ramirez during the summer for a club record fee of £12 million from Bologna, but he is yet to live up to his billing after just three goals and no assists in 13 Premier League appearances - though injuries have hampered his progress.
Milan are currently looking to add to their squad as they continue their rebuilding, but Galliani has ruled out a move for the Saints No.10, adding that expensive signings will only be brought in if other players are sold.
Speaking to Sky Sports Italia, Galliani said: "There’s no need for Ramirez, we are fine as we are. If someone leaves then we’ll see, but there are no 'gifts' on the horizon for the fans."
One player Milan do look poised to bring to San Siro is midfielder Riccardo Saponara, who is currently co-owned by Empoli and Parma. However, an agreement could be reached to purchase Empoli's half of the contract for around £3m.
"Saponara is certainly a player that fits in with the policy of focusing on youth that Milan are taking," Galliani noted.
Fellow Serie A sides Juventus and Inter, as well as Liverpool, are believed to be interested in the creative midfielder, but Empoli's director of sport has also confirmed Milan's interest.
Speaking to Calciomercato, Marcello Carli said: "It's true, there is a deal with Milan for half of Saponara's contract.
"He was tracked by many clubs, but the Rossoneri were quick off the blocks. The player will remain with us until the end of the season. That was a decisive factor in negotiations."