Reports in Italy have claimed that Milan want to replace Antonio Cassano with Stamford Bridge star Drogba this summer.
Cassano is a reported target of Serie A side Fiorentina.
However, Galliani has told Corriere dello Sport: "We are covered in attack and hence, Drogba will not arrive."
Fernando Torres' big-money move to Chelsea in January led to growing speculation that Drogba could leave the west London club this summer.
The 33-year-old, who is under contract with the Blues for a further year, endured a disappointing second half of last season, scoring just four goals in 20 Premier League appearances.
Source: Team Talk
Source: Team Talk