Former Chelsea midfielder Cole has been linked to Milan, as well as a number of clubs in England, after he fell out of contract at Stamford Bridge.
However, Galliani is adamant the Rossoneri have no intention of signing the 28-year-old - despite the fact he would not cost them a fee.
He said: "What would we do with Cole? Milan have a very complete squad."
Galliani also insists the club are unlikely to move for Luis Fabiano, amid speculation he is set to move to the San Siro after his agent declared that "either he goes to Milan immediately or he stays at Sevilla one more year".
The 29-year-old has one more year left on his contract and, if he does not renew, Sevilla would prefer to sell him this summer than risk losing him for nothing at the end of the season.
Galliani, however, is remaining tight-lipped.
"Let's leave Luis Fabiano be, he's playing in the World Cup and belongs to Sevilla. There are no negotiations going on," said Galliani.
"In order to come here a great or very great player has to leave Milan. And for me Luis Fabiano is a very great player.
"However, we don't make big-name players leave."
Galliani insists Milan have to sell before they buy.
"The arrivals have to be in proportion to those who leave," continued the Milan boss.
"I'll summarise: Dida left and (Marco) Amelia came, (Giuseppe) Favalli left and (Mario) Yepes came, more in general if a big-name leaves a big-name comes, if a lad who completes the squad as a 24th man leaves then a lad comes in who is able to be the 24th man.
"But the big, big, big, big-name players, we don't sell them for our choice."