That being said, general manager Brian Cashman may end up looking for a replacement if another team sweeps in and offers Cano an exorbitant amount of money. The Yankees have already stated that Cano is not a "re-sign at all costs" kind of player—you can debate that amongst yourselves—and an asking price of over $200 million will likely deter Cashman from negotiating with him.
The departures of Mariano Rivera and Andy Pettitte—coupled with the potential loss of Derek Jeter after next season—would leave Cano as the unquestioned face of the franchise for the foreseeable future. He's extremely valuable and difficult to let go, as he has been the Yankees' best player for the better part of the last five seasons.
Letting him walk would thrust the Yankees into an instant rebuilding mode. The team would not be nearly talented enough to make a run at the playoffs, and that would represent the official end of an era in New York.
The options to potentially replace Cano come via free agency because of the position's lack of depth in the Yankees' system. Second base isn't a particularly talented position down on the farm, and it'll be a few years before anybody is ready to make an impact.
The options aren't great in free agency, but Cashman will have to sign somebody to play second.