Only person who can do that is Murphy, and I don't think Murphy wants to meddle like that. Firing MLF would have been a big headline and a bad move, he called some good games in the latter part of the season and kept a young locker room together when they were in danger of circling the drain.
I doubt they would play that kind of brinksmanship.
I do wonder, based on Gute's comments after the draft, if there was some kind of discussion b/t Murphy, Gute and MLF about the defense last Spring along the lines of - we have a young offense, we have a lot of high draft picks on defense; if the defense can't hold the fort and win some games Barry has to go. It's fair to say by the 3/4 point of the season the offense was carrying the defense, not the other way around. Expectations for the defense were higher this year, and I don't think they performed significantly better.... getting a warning and still not meeting the expectations can be grounds for termination in a cutthroat field like coaching.