Spagnuolo, one of the team's top candidates, also met Thursday with Cleveland and Detroit about their openings, and was scheduled to talk to Denver on Saturday night.
The Jets spoke with current assistants Bill Callahan and Brian Schottenheimer on Friday in the first round of interviews since the team fired Eric Mangini on Monday. No other interviews were scheduled as of Saturday night.
New York received permission to speak with Baltimore defensive coordinator Rex Ryan, but won't be able to meet with him until the Ravens' season is over or during the bye before the Super Bowl, if they make it.
The Ravens play at Miami in the playoffs on Sunday.
Similarly, the Jets wouldn't be allowed to offer Spagnuolo a job until the Giants' season ends. The NFC's top-seeded team has a first-round bye in the playoffs. Spagnuolo, 49, has become a popular candidate because of the Giants' success on defense the last two seasons.
He turned down the Washington Redskins job last year after being lauded for the pass-rushing game plan that stunned Tom Brady and New England in last year's Super Bowl.
Owner Woody Johnson is out of the country and was not involved in the interviews conducted by general manager Mike Tannenbaum, but is said to be in constant contact with him regarding the coaching search.
Johnson has made it clear he prefers to keep football, business and coaching duties separate, so any coach the Jets hire would have to fit into that structure.
That prerequisite likely cooled New York on Mike Shanahan, fired Tuesday night by Denver. Shanahan went 146-91 over 14 seasons, including the playoffs, but was also the team's executive vice president of football operations. He told the NFL Network he planned to wait two weeks before speaking with a team about any opening.
Bill Cowher, thought to be the Jets' early No. 1 target, pulled his name out of consideration late Tuesday night. The former Super Bowl-winning coach with Pittsburgh has said he's not interested in returning to the sidelines before 2010.
Browns’ search starts with McDaniels, Tucker
Canizares: Tottenham Didn’t Understand Juande Ramos
Jets interview Callahan, Brian Schottenheimer
