Is Mike McCarthy possibly the Saints next head coach if Dallas lets him walk?

BTW, I would put Belichick more in the anomaly category then Reid. A decade ago, Andy Reid was sort in the same position as McCarthy is right now: very good, consistently-winning HC who had won a lot of games but unlike even McCarthy, hadn't won the Super Bowl or was criticized by his detractors in Philly and even early on in Kansas City that he couldn't advance past a.certain point in the post-season. He could make very good QB's look better then they really were but until he found "his guy" "his Tom Brady" in Patrick Mahomes, he'd only won one post season game as Chiefs HC. When he found his "Brady", this almost-mythical, superhuman duel-purpose QB, he found a way to maximize every possible aspect of talent he knew existed in Mahomes, plus he had a great supporting cast already in place.He's not really an anomaly, he just finally found that guy who makes the pieces all fall into place and can still succeed whenever it screws up sometimes. McCarthy had that sort of superstar QB in Aaron Rodgers for over a decade and aside from one SB win, he left quite a few wins in the regular-season and post-season on the table.
Jones doesn’t get a say in it other than the offer he makes Mike, which, that is a big part of it. However, if Mike wants to leave there’s nothing that can be done.

Hopefully he stays put.
The only reason why I can see Jones staying with McCarthy a few more seasons at best is because he still remains his best overall choice as HC. Belichick likely would be the incoming HC if his price, and his overall demands for on-and-off team personnel control weren't too high and ego-bruising for Jones and his family to tolerate or allow and maybe Mike Vrabel likely doesn't want his second HC coaching stint dominated by being another "puppet HC" of Jerry Jones in Dallas.

If Belichick had allowed himself to be more amenable and not demand the same level of power, influence over personnel issues as he did in New England but knowing those two men's enormous, meglomaniacal egos and maybe based partly off his frustrating experiences butting heads with Bill Parcells, Jones doesn't want to re-create those same experiences again and he's not getting any younger.