The San Siro side are desperate to add some fresh blood to their squad and have set their sights on the Chelsea striker and midfielder
Head coach Filippo Inzaghi's side are in the market for attacking reinforcements following the departure of Mario Balotelli to Liverpool and they see Torres as the ideal replacement.
The 30-year-old appears to be surplus to requirements at Chelsea due to the arrival of Diego Costa and Milan are hopeful of signing the Spain international on a one-year loan deal.
"We are approaching the final stages of the transfer window. Let's see whether we can sign a top striker. That's our most important objective at the moment," Galliani said.
"Torres is definitely a top striker. We will see whether we can sign him or another attacker."
The chief executive then went on to discuss the potential signing of fellow Chelsea midfielder Marco van Ginkel and acknowledged that Milan have made a formal offer for the Dutchman.
"Signing Van Ginkel seems a realistic possibility. We have submitted an offer to Chelsea. We now await their response, but we are fairly optimistic."
The 21-year-old joined Chelsea from Vitesse last summer, but was unable to make an impact in his first season at Stamford Bridge due to a knee injury he suffered early in the season.
Chelsea are believed to be open to sending him out on loan in order to gain valuable first-team experience in one of Europe's elite competitions.