The Jets are expanding their search for a new general manager, setting up interviews with Miami assistant GM Brian Gaine and Pittsburgh executive Omar Khan.
New York previously interviewed David Caldwell, hired by Jacksonville, San Francisco's Tom Gamble, the Giants' Marc Ross and Jets assistant GM Scott Cohen. Gamble had previously been considered the front-runner for the job, but has also drawn interest from other teams.
Mike Tannenbaum was fired by owner Woody Johnson on Dec. 31 after seven seasons as the Jets' GM.
Idzik has overseen player negotiations and the Seahawks' salary cap for the last six years.
Johnson confirmed Tuesday in his first meeting with the media since firing Tannenbaum that the team has told candidates they must be willing to work with coach Rex Ryan.
"They know he's a good coach and you can't always say that," Johnson said. "It takes one of the uncertainties out of the equation."
Johnson also added that Ryan would be part of the process to find the new general manager.
"I'm pretty sure I'll have the exact same agenda that the general manager will have and that's, we want to win," Ryan said Tuesday. "I know that I don't know who the general manager is, but I promise you, he wants to win as bad as I do and that's something certainly we'll lean on."
The Jets are using Jed Hughes of the search firm Korn/Ferry International to aid in the process of identifying candidates.
New York is also in the market for a new offensive coordinator after Tony Sparano was fired on Tuesday. Ryan announced that Mike Pettine wouldn't return as the team's defensive coordinator, and defensive backs coach Dennis Thurman is expected to be promoted to the position.