The Netherlands midfielder was linked with a move away from the Serie A club during the close season, with Manchester United reported to be interested in signing the 29-year-old.
However, he has no intention of leaving Milan and wants to be part of the revolution under Filippo Inzaghi.
"I want to stay at Milan and I repeat that I want to end my career here," he is quoted as saying by Tuttosport. "Milan is a club with a history and an extraordinary tradition - if they cannot finish first then they must always fight to be in the top three.
"I know it is tough, I know that there are many teams as strong and organised as we are, but we have to try.
"At what point is the new contract? I know that the club has contacted my agent and there is an appointment for next week."
Milan have won both of their league matches this season and face defending champions Juventus on Saturday.
De Jong is convinced Inzaghis's men can compete with the Turin giants.
"Juve have won the league title in each of the last three years - we do not have to discover them," he continued. "In the Champions League they won and with conviction.
"To have the chance of success we must begin fighting from the first minute. Will it be the first real test for the new Milan? Certainly, but it will also be for them."