Ibra was linked with Manchester City yesterday.
"He said he loves Milan and fortunately for us he has also said that he will remain at Milan," Allegri told Rtl 102.5.
"I have Ibrahimovic and Thiago Silva and am lucky enough for this, without taking anything away from those who are leaving the club.
"I think Milan have had 10 years of these champions, especially Italians, and at the greatest level. Unfortunately of the current champions, fewer are Italian, which is bad for Italian football.