Barry has spent this season on-loan with Everton.
The People says NYCFC will compete in the MLS from next season and are considering a bid to make Barry one of their three marquee players.
Should Barry agree to sign for the New York club then he will also look for a side to join on loan in the Premier League until the end of January, when he would jet off across the Atlantic.
Everton would be interested in taking him on loan for the first part of the season and the fact he is not joining them permanently means there would be no fee.
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