Abate has attracted interest from Zenit St Petersburg, while Boateng was in crunch talks at Milan HQ earlier in the day.
"I can say that Boateng is going nowhere, even if there have been rumours of a Galatasaray offer. He is only 25 years old and will not be leaving here," assured Galliani.
"Boateng is a part of the present and the future of Milan. Galatasaray were here to talk to us for different reasons. Nobody has asked us for Boateng and if an offer were to come in, we would say no.