The 29-year-old midfielder has been a regular at San Siro this season, featuring 20 times in Serie A and scoring two goals.
Milan have endured a difficult season and currently sit 10th in the league, a massive 34 points adrift of leaders Juventus and six behind city rivals Inter - who occupy fifth spot.
Montolivo's representative, Giovanni Branchini, claimed the likes of Atletico Madrid, Borussia Dortmund and Arsenal had all made enquiries to prise him away from Italy.
But he suggested Montolivo is not seeking pastures new.
Speaking to calciomercato.it, he said: "There have been a few polite enquiries.
"From Atletico Madrid, Dortmund and Arsenal to name a few. All of them wanted to know whether Montolivo was available.
"At the moment though, I really do think it would be very difficult to see the player leaving Milan.
"Milan have had a troubled season and I think I can say that he has been one of the highlights.
"He has become an important part of the Rossonero starting line-up this season. He is very happy with the club he is at, and the club and the fans are very happy with him.
"He has a contract until June 2016 so it is not a priority to talk about a renewal just yet. It's something we will maybe discuss next year."
