Speculation has been rife that the goalkeeper could exit San Siro in the summer, but it now appears he will extend his 15-year stay at the club.
The Italian shot-stopper has been a San Siro player since 1998 but has spent stints on loan with the likes of Juventus and Atletico Madrid, and Galliani has insisted that a new contract with the Rossoneri is just around the corner for Massimiliano Allegri's No. 1.
"There is no doubt that the contract will be renewed for Abbiati," Galliani told reporters on Tuesday. "He is one of the most important elements of our team that we never questioned not renewing, it only lacks the signatures.
"Against Torino he gave yet another signal of his value to us; we do not want to deprive ourselves of what he brings to the team."
Milan is currently four points clear of Fiorentina in third place with three games to go and could secure a Champions League berth if it beats Pescara on Wednesday and the Viola lose at Siena.