The Belgium international, valued at around €14 million (£11.6m), is a highly sought-after midfielder, with the Rossoneri, Juventus, Napoli, Giallorossi and other European clubs interested in acquiring his services.
However, Galliani says there is only one destination in his mind where the 25-year-old is heading.
"Nainggolan will not be going to Milan,” Galliani told Sky Sport Italia. “I believe the bidding war to be over, anyway.
“If I had to bet – not that I can, because I’m a club director and we’re not allowed to – but if I had to indicate an option then I’d say he’s going to Roma. As far as I know, that is the situation.”
Milan, 18-time Italian champions, have already signed Adil Rami and Keisuke Honda in January as they look to improve on their current position of 13th in Serie A.
However, further arrivals look improbable until players leave San Siro, with Galliani keen to avoid an over-staffed squad.
He told reporters: "Currently our squad is at 30 - we need to thin that out by two or three players, then we will see if a midfielder can arrive."