Grant was named Pompey’s director of football earlier this week.
“Grant would make history in New York based on the demographics of the area,” Don Barnett told the New York Times.
“With all the Jewish residents and expat Israelis in the area, coupled with his profile at Chelsea, he would have raised the profile of Red Bull to a higher level on and off the field – and helped to sell tickets and attract players.
“He wants the job but I guess he couldn’t wait on them any longer.”