Reports in Italy had suggested that director Barbara Berlusconi spoke with father and club president Silvio about making changes within the staff following Sunday's 2-0 defeat to Fiorentina.
Ms Berlusconi responded to the reports by stating that she "never asked" for Galliani to be replaced, insisting she simply requested a "change of business philosophy" at the club.
Sunday's defeat means Milan are three league games without a win, with Galliani admitting the poor run of form has made life tough for the club, although he would not be drawn on goings on behind the scenes.
"It is a difficult time because the results don’t seem to be coming," he told the club's official website.
"We will move on and hope that things get better. Today I only intend to speak about footballing issues, I have no intention about commenting on anything else; there is no comment.
"The chief executive is responsible for everything, transfer policy, revenue, accounts, everything. I have spoken a lot to the president, including last night."
Galliani also backed manager Massimiliano Allegri to turn results around, explaining the Milan board has "absolute confidence" in his ability.
"Our side is worth more than what the league table suggests, Milan is a side on par with recent seasons and our ranking," he continued.
"In the last 12 years, we have taken part 11 times in the Champions league. You cannot judge a club solely on the last game played. At the moment the results are not coming. But in these times my experience teaches me that we need to stay calm.
"As for the rest, we will analyse at the end of the season. There is absolute confidence in Allegri. Naturally, all coaches are dependent on results. If a coach constantly loses then obviously that isn’t good enough, but I don’t think that this will be the case for us."
