The CEO of the reigning Serie A champions has admitted that he is interested in luring the striker to San Siro.
Former Chelsea manager Carlo Ancelotti urged Milan earlier this week to make a move for the duo, and Galliani has now admitted that he's been a long term admirer of the Cote d'Ivoire international.
"Ancelotti is someone who knows his football. Perhaps we will sign both players," Galliani said to La Gazzetta dello Sport. "Anelka is a great player, however, I have dreamed of signing Drogba ever since he played for Olympique de Marseille."
Anelka's current contract with Chelsea is due to expire at the end of the season, while Drogba, 33, has an expiring deal as well.
"Seriously though, we don't know yet whether we will sign someone in the January transfer window. If so, it will be on a loan deal."