Fizdale is New York's 11th head coach since the 2001-02 season, and the fifth since the start of the 2010-11 season. He had one year remaining on his contract.
Fizdale went 50-51 in 101 games as head coach of the Grizzlies before being fired 19 games into this season.
Fizdale met with the Suns about the vacancy, per 98.7 FM Arizona's Sports Station's John Gambadoro.
After winning 43 games and leading the Grizzlies to a postseason berth in his first season as head coach in Memphis, Fizdale was sacked just 19 games into his second campaign amid reports of a rift between him and starting center Marc Gasol.
Former Atlanta Hawks Mike Budenholzer met with the Suns' front office and ownership for two days before withdrawing his name from consideration.
The Knicks then conducted a lengthy search before agreeing Thursday (Friday, Manila time) to a deal in principle with Fizdale, the person told The Associated Press on condition of anonymity because the deal was not officially announced.
Fizdale went 43-39 and led the Grizzlies to the playoffs in his lone full season in Memphis.