First of all, the Sox can't make an offer to any free agent until 15 days after the conclusion of the world series ... so November 20th at the earliest.
Second of all, he's pretty much a DH only at this point so I don't really believe this. I'd say it's just posturing by his agent for the NYY to lock him up to a contract by saying "If you don't sign him, your rival to the north will, there's already a multi-year contract offer on the table from Boston"