The English side are the main owners of the MLS club, which would facilitate an easy arrival for the former Barcelona player to the United States.
According to a report by ESPN, the New York team are already negotiating a transfer for the Ivorian man.
It is reported that the American team is aiming for the 34-year-old player to make his debut in the 2018 season.
However, at the moment, Manchester City coach Pep Guardiola wants to keep hold of Toure until the end of the Premier League season, when his contract expires.