"From my understanding, Ryan's asking price is still very high, around $10 million. The Jets are not doing that," Costello wrote.
Costello previously reported the Jets met with the cornerback's representatives but did not make a formal offer.
After spending the past three seasons with the Tennessee Titans, the 29-year-old announced he will not re-sign with his team.
"My chapter in Tennessee has come to a close," Ryan wrote May 5 on Instagram.
The two-time Super Bowl champion with the New England Patriots is coming off arguably his best season in the NFL.
Ryan led the Titans with 113 tackles while filling up the stat sheet with four interceptions, 18 passes defended, 4.5 sacks and four forced fumbles.
The New Jersey native should clearly help a Jets defense that ranked second in the NFL against the run but only 17th against the pass.
New York moved on from cornerbacks Darryl Roberts and Trumaine Johnson this offseason, leaving the team especially thin at the position. Even with the addition of Pierre Desir in free agency and fifth-round draft pick Bryce Hall, the squad could still use more depth in the secondary.
The team still has $11.9 million in cap space, per Spotrac, and will apparently try to get Ryan to lower his asking price before making a deal.