Reports in the media have linked the Brazilian with a big money move to Paris St Germain.
The transfer talk has intensified since the striker's former boss Carlo Ancelotti took over at manager of the French club. The rumours have gained even more momentum after Pato criticised Allegri, saying he needs to give him more direction.
However, Allegri has claimed that he wants the 22-year-old to stay.
"There has never been a problem between me and Pato," said Allegri.
"If there was then it's been resolved.
"I think he'll stay at Milan, I want him to stay at Milan."
Pato joined Milan in 2007 from Brazilian side Internacional after making only 10 appearances.