Seedorf-Coco deal agreed
The reports have been circulating for some time, with Inter president Massimo Moratti recently admitting the stories hold some truth.
Galliani has now revealed the talks have advanced, with both teams set to speak with the other`s player in a bid to thrash out personal terms.
Speaking on Milan`s official website, vice-president Galliani said: "The two clubs have agreed a straight swap involving Francesco Coco and Clarence Seedorf.
"The only issue remaining is the wages for the two players. We have authorised each other to contact the respective players.
"Milan will speak with Seedorf, while Inter can now start talks with Coco."
The deal is far from cut and dried, as Coco is currently on loan at Barcelona and has continually stated he wants to turn his temporary stay at Camp Nou into a permanent arrangement.
The Catalans, though, are unlikely to take up their option to sign the player, which expires on Friday, and he may then consider a move to Inter.
Dutch international Seedorf may take some persuading, as he has been a key figure for Inter and it could be a wrench swapping the Nerazzurri for the Rossoneri, but if he feels he is wanted elsewhere the transfer may be concluded.