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."
Manchester United eyeing surprise move for AC Milan star for whom tension in Italy is growing: report
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
