Well it seems that David Stearns has already answered my question! Here it is:
“He’s a great Met,” Stearns said. “I hope we have him back. I think we both understand this is a process and everyone’s got their own interests. And Pete deserves to go out into the free agent market and see what’s out there and ultimately make the best choice for him and his family.”
Translation: "Pete, I really like you, but I think maybe we should see other people. Y'know, just for a while."
If you really want to marry the girl, that is NOT how you go about it.
Could Alonso still re-sign? Sure. The Mets took the same approach with Nimmo. They let him define the parameters of the market, then swooped in with their offer.
But clearly Alonso is not on top of the Mets list. If he were, Stearns and Cohen would be doing all they could to make sure that Alonso does NOT see what's out there.