The new MLS franchise won't be playing until next March.
NYFC chief and former Manchester City midfielder Claudio Reyna said: "This is the perfect opportunity for Frank. He is in great shape following the World Cup, and training and playing with our colleagues in Manchester will enable Frank to be fit and ready for our inaugural training camp.
"Everyone has been hugely impressed with Frank's positivity, and I'm sure he will bring a lot to City during his stint with the club.
"We wish him well for his spell with Manchester City and look forward to welcoming him back to New York in the New Year."
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