Several media outlets in Italy have suggested the Rossoneri directors cannot agree whether or not to retain head coach Massimiliano Allegri, with Galliani supporting the Tuscan tactician while Berlusconi looks for a replacement.
Allegri secured the Serie A title in his first season in charge but followed up last year's second-placed finish with an inconsistent campaign that saw the Rossoneri only book third place on the final day.
While Galliani would not comment on suggestions his long-term collaborator is lining up former Milan midfielder Clarence Seedorf to take the reins at San Siro, he stressed their professional partnership is not at risk.
"My personal and professional relationship with Silvio Berlusconi dates back 33 years," he told acmilan.com.
"The mutual affection and respect has never been cracked by the normal disagreements that happen in every personal or professional relationship, neither in the past nor today, contrary to what I read."
Wednesday saw leading Rossoneri supporters group Curva Sud Milano question the potential appointment of Seedorf, with a lengthy statement accusing the former Holland midfielder of having "no experience".
The group also recognised Allegri as the "driving force" behind the large-scale rebuilding project required at the club after several high-profile players were sold last summer.
A statement on curvasudmilano.it read: "The careful management of coach Allegri, who we recognise as the driving force behind the project, allowed us to climb from second-bottom to third place with only one high-profile addition - Mario Balotelli in January.
"Today we find ourselves at the beginning of a project which could soon be dismantled because of the president's choices.
"We understand that he who has made investments can decide to change coaches for personal reasons, but you must start a new project with a recognised coach and not someone like Seedorf who has no experience ahead of an engagement as difficult as the Champions League qualifying rounds."