Rich Cimini of ESPN reported the Jets' interest, noting that they would have to win a "bidding war" for both players.
Jones, 27, recorded 36 tackles and six passes defensed in 2019. Those numbers were markedly down from his Pro Bowl campaign in 2018, which saw him record 67 tackles and 14 passes defensed.
Bradberry, 26, had a far stronger 2019 with 65 tackles, three interceptions and 12 passes defensed. His strong season was a little overshadowed by a lost Carolina campaign.
The Jets have a recent history of trying and failing to sign a shutdown cornerback in free agency. As noted by Cimini, they spent a combined $74 million guaranteed on Darrelle Revis (2015) and Trumaine Johnson (2018) only for both to wind up being cap albatrosses.
Jones and Bradberry are each expected to command top cornerback money when free agency opens March 18. Adam Caplan said on the Inside the Birds podcast the Eagles are going to be "all in" on signing Jones, while Cimini notes Washington may target Bradberry with former Panthers coach Ron Rivera now with the Redskins.
Should the Jets find a cornerback capable of covering top wideouts, they could have one of the best defenses in football. The Jets finished second in run defense DVOA last season and 18th against the pass, per Football Outsiders.