Reports yesterday suggested that the two men had a row and exchanged insults while the tactician visited the club's youth sector.
"Nothing happened, absolutely nothing," Allegrisaid. "There is no problem with Pippo. In fact, there is great collaboration between the first team and the youth sectors. There was an exchange of opinions without any offence or heavy words."
Inzaghi, new boss of the club's Allievi side, backed up the claims of the former Cagliari Coach.
"Allegri is right, it lasted for one minute," he stated. "The youth team players didn't notice anything because nothing happened.
"We are Milan and we all love Milan, so nothing like that would have occurred. Rather than writing about things that didn't happen, Milan need a helping hand."