Bowles told ESPN that he was taking the job, but the person told The Associated Press that no agreement had been completed as of late Tuesday night.
The person spoke to the AP on condition of anonymity because the deal had not been finalized.
A few hours after hiring Mike Maccagnan as their general manager Tuesday, the Jets were closing in on signing the 51-year-old Bowles to replace Rex Ryan, who was fired, along with GM John Idzik, on Dec. 29 after six seasons.
Bowles was a highly sought candidate after leading Arizona's defence the last two seasons.
AP NFL website: www.pro32.ap.org and www.twitter.com/AP_NFL