Allegri has been in charge of Milan since 2010, but reports have claimed he could be appointed as the long-term replacement for Zdenek Zeman at Roma at the end of the season.
However, Allegri has brushed off the speculation and is focused on ensuring Milan qualify for the UEFA Champions League again, with the club currently third in Serie A.
"I have a contract with Milan until 2014," Allegri told Sky Italia. "The president had positive words for me, the club too.
"I think that sometimes, whoever writes certain things becomes a little boring. We will see.
"Anyway, our aim is to finish the season and hope that my guys will take us to second or third place. Then we will see.
"I'm really happy to stay at Milan, but to stay together, there is the need of both parts. From my side, I feel a big faith from the club.
"Getting a place in the top three this season will be really important."