The Brazilian returned to San Siro last summer from Real Madrid but it had been reported he would move on if Clarence Seedorf's side were to fail to qualify for Europe.
However, the playmaker says he wants to stay put and is enjoying working under the Dutchman, who succeeded sacked coach Massimiliano Allegri in January.
"I personally have done well but it hasn’t been enough in the general context. I can improve for next year and my intention is to stay," he told Tiki Taka.
“I like the club, I am used to other things, but the situation is this and we must live it, plus, we have this special derby to play.
"I do not even want to remain anxious and wait too long, the fans can rest easy because there are no games or anything, it will be a personal choice and that of my family, but the biggest desire is to stay.
"He (Seedorf) is definitely starting on a different career, but I do not see him as a different person, you must understand that many things that a player sees in one way, a coach will see in another.
"He is very good and very smart, he will learn everything quickly. I am really happy working with him, he can achieve great things."
Milan currently sit 10th in Serie A, but only one point separates them from sixth-placed Torino.