Originally Posted by PatsFanTX
Yes, but the Jets FO has to give their permission.
Otherwise, it would be considered tampering.
It's a bit more that that though. The contract can't be (officially) renegotiated until the player signs with the other team. That means the other team has to have the cap room to absorb the original salary. Then, once the player signs, they can tear up the contract and make a new one.
This happened when Moss was traded to the Pats. They had to make room for his original salary before drawing up the new contract.