"I told these guys we are not trading up this year," the general manager said last week while on a dais with senior personnel executive Terry Bradway and Joey Clinkscales, vice president of college scouting.
"No matter what happens, grab the phones," Tannenbaum said with a laugh. "I don't want to trade up, but we'll see what happens. I think we're happy with where we are, but we'll let the board dictate what we do. I like where we are. I want to keep our first two picks where we are. We should get two good football players that can help us."
Tannenbaum left the door slightly ajar to move up from No. 29 - the first of five selections the Jets hold. He's been a trading machine during the draft, moving up three times in four years to pluck a player he thought he couldn't pass up.
Last year, Tannenbaum worked his magic with show-stealing trades again, acquiring the Browns' fifth overall pick so he could draft Mark Sanchez. Then he shipped three picks to the Lions so he could use the second day's first selection on Shonn Greene.
But don't expect the Jets to be on the offensive so much this year. They've addressed needs at running back and wide receiver by bringing in LaDainian Tomlinson and Santonio Holmes, so upgrading their top-ranked defense probably will be more of a priority.
Either way, the Jets' busy offseason gives them a bit of flexibility and provides more of an opportunity for Tannenbaum to come up with yet another draft-day trade.
"We have an excellent football team," Rex Ryan said. "There's no 'You absolutely need this or you need that.' We're set up. We're in an ideal situation and that is we have a great team. We're going into the draft where we can take the best player. That's where you usually make the best decisions.
"Usually when you make mistakes in the draft, it's all about reaching for a guy or a need and you let a football player go by. The fact that we have the draft coming up and we already have a great team, it's going to be a real positive for us."