The Jets tried to sign Callahan to an extension, even recently, but he decided to keep his options open -- and now he could have leverage. But that's not the story right now; the story is Schottenheimer and how the Jets' offense has gone into the dumpster the last two weeks.
Callahan might want to be an offensive coordinator. Remember, the Jets denied him a chance to interview for a coordinator job with the Titans last year. If he is under contract, the team can decide whether to make him available. In the NFL, a move from position coach to coordinator is considered a lateral move.
It sounds like the Jets might lose Callahan as offensive line coach. If they want to keep him, they might need to make him offensive coordinator. It would be a loss. Look at the record. The Jets developing into a top run team ran parallel with his arrival. D'Brickashaw Ferguson was a disappointment when Callahan arrived. Some even called hima bust. People grumbled about Brandon Moore getting a contract extension in 2007 because Moore was viewed as mediocre. Damien Woody went from being a guard who was benched the year before he came to the Jets with just a bit of tackle experience into one of the best right tackles in the league. Matt Slauson has developed into a good starter.
This year the line hasn't been at its best with Wayne Hunter. Even then I think there is a case to be made that Callahan has had a positive impact. Hunter has gone from a guy who has pretty much been a zero during his career into a guy who has been passable at times and played well in brief stretches. His ceiling is just very limited.
Even discounting this, the Callahan record has been much more good than bad. He is an accomplished position coach, though, and has a good track record as a coordinator. I think his loss would be felt.