New York is conducting an exhaustive search with multiple interviews already conducted, and more on the way on top of Angelo's, by all accounts.
Angelo was the general manager of the Bears for more than a decade, from 2001-11. He oversaw the hiring of Lovie Smith in 2004, who lasted with the team until this offseason, when he was let go after the Bears missed the playoffs with a 10-6 record.
He was let go in 2011 due to what the organization felt was stagnation and a lack of production in the NFL Draft. The team stated they wanted to "close a talent gap" within the division when speaking on Angelo's firing.
The Jets have a huge list of candidates thus far, including David Caldwell, Scott Cohen, Tom Gable, Tom Telesco, Jimmy Raye and even more on top of that. Head coach Rex Ryan remains in place, though there are still decisions to be made regarding some of the assistants on the coaching staff.
For a look at all the candidates, stick with this stream.