According to Manish Mehta of the New York Daily News, before trading up to No. 3 overall, the Jets had inquired with the Cleveland Browns about moving up to No. 1 overall.
The assumption would be that the Jets wanted to guarantee their choice of a quarterback. One would also think that because no deal happened, that Cleveland is locked in at No. 1 overall to select their quarterback of the future. And if Cleveland’s asking price was just a little too high for the Jets, I think they would’ve given it up.