The midfielder's current contract expires at the end of the year, and according to Aftonbladet, he will stay in New York, where he is team captain, until the summer.
The 35-year-old Forsberg moved to New York three years ago after many years at sister club RB Leipzig in Germany. He has scored 25 goals and provided 16 assists in MLS.
Last summer, Forsberg announced that he was ending his international career. He scored 21 goals in 92 appearances for Sweden.
