The veteran midfielder's 18-year stay at AC Milan will be coming to an end when his contract expires, with Riccardo Montolivo set to replace him as captain.
The 36-year-old joined the Rossoneri from Cesena back in 1995 and has been at the club ever since, barring a loan spell at Vicenza in 1997-98.
He was named skipper in 2009 following the departure of defensive stalwart Paolo Maldini but his time at the Giuseppe Meazza has now come to an end.
"Milan will part ways with Ambrosini," Galliani told Sky Italia.
"Our next captain, if [Christian] Abbiati agrees, will be [Riccardo] Montolivo."