By ESPNSTAR.com staff
Milan president Silvio Berlusconi was said to have arranged for a meeting with Galliani after the defeat to Fiorentina on Sunday, during which Allegri's future was a serious topic of consideration.
With Allegri's Milan having only secured 14 points from their first 12 games of the season, many in the Italian media have called for a managerial change to help steer the Rossoneri back on course.
The 45-year-old is still held in high esteem by the club hierarchy, however, and they understand that the team is struggling to deal with the departures of key players Thiago Silva and Zlatan Ibrahimovic over the summer.
"There is absolutely no time limit to this backing," Galliani specified when questioned by La Gazzetta dello Sport if he had changed his mind over his earlier show of support for the Milan coach.
"We are of course not at all happy with the situation, but we assessed everything and we are not certain that things would improve were we to change the coach.
"Besides Allegri has done a good job in the two years he has been here and so that is the decision."
Milan face Napoli in the Serie A on Saturday in what will be a must-win clash for the former Cagliari coach.
And the Rossoneri face an equally crucial encounter with Anderlecht in the Champions League next week with the Belgian champions just one point behind in Group C. The duo are vying for the remaining qualification berth after Malaga progressed to the last-16 with a 1-1 draw against Milan at the San Siro.