My feeling, based on nothing but my feeling, is that Jerry probably prefers to keep McCarthy, but on a short term deal, say 2-years, maybe 3, that wouldn't be that painful to piss away if he decides to cut bait during or after next season. He has injuries and the transition to the new defense as excuses, and the team showing some backbone as lame ducks as support for their coach.
McCarthy may not be willing to take a deal like that. All the rumored interest in his services by other bottom feeding teams with vacancies may be legit, or not. The teams that are showing interest are some of the biggest dumpsterfires, so he probably prefers to stay, which gives Jerry a little leverage in negotiation.
There's no reason to give the Bears or anyone else permission to speak with McCarthy. It's only another week or so before he can do whatever TF he wants. Meanwhile, the Cowboys can kick the tires on other available coaches behind the scenes.
If they bring him back, I would hope they bring in some better training wheels, like offensive coaching talent that bring more imagination to the offense, maybe some much better scouting in certain areas where they tend to suck ass. A potential younger head coach in waiting prospect would be nice, too. The staff is too damn old and out of date.