Xavi is widely expected to leave Barcelona in the next couple of weeks, with a move to the MLS heavily suggested in various quarters.
Bover has welcomed such interest and admitted that talk of the Spanish international's arrival has gripped the city as a whole.
"In New York they are talking about the arrival of Xavi," Bover is quoted by La Xarxa.
"But until it becomes official I don't believe it. You hear so many things. But it would be great to see him play in his final years. If Xavi comes it will be a real treat for the league, for the fans, the clubs. The league continues to grow and I would recommend that he comes to New York Red Bulls.
"Coming to New York, or to [New York City FC] he will love. I'm sure he will love New York. I don't know about Seattle. The experience in New York is very good, so worth it, highly recommended."
Xavi has also been linked with a move to Qatar.