De Jong joined Milan from Premier League outfit Manchester City in 2012, signing a three-year deal.
A mainstay in the Milan starting XI, De Jong has made 32 appearances in all competitions this season for a side that has struggled for form in both domestic and European competition.
Despite Milan's below-par campaign to date, the former Ajax man is eager to extend his stay with the 18-time Italian champions.
"I want to try and stay at Milan for another four or five years," De Jong told Bild.
De Jong spent three years with Bundesliga club Hamburg before making the switch to City in 2009.
Asked about the possibility of potentially returning to the Imtech Arena in the future, he added: "I have a lot of time for that club. And I have always liked it in Germany."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.