Mourinho has alienated players, fans and staff alike this season - he has been at loggerheads for weeks with World Cup victor Paul Pogba - and it seems the United board, led by executive vice-chairman Ed Woodward, now want to make a change.
United, though, have not challenged for a Premier League title under his watch - they finished sixth in that first season, 24 points behind champions Chelsea, and though they were runners-up last term they trailed rivals Manchester City by 19.
"We can do much better", he explained in his pre-match press conference.
World Cup victor Pogba is among those to have been dragged into a distracting series of rows, with the Frenchman considered to be failing to reach his potential as a result of having the wrong manager guiding him.
Neville, who played his entire club career at Old Trafford, questioned the "values and principles" of the club if Mourinho were to be sacked. I have to say something has to change and it isn't the manager, it's above that. I absolutely love it to death.
He starts by saying: "I'm furious from three or four years ago when David Moyes was sacked and it was broken a day before to journalists".
"Because look, at the end of the day this been going on for five or six years, and I have to say that any manager".
Turning his attentions to Saturday's 5:30pm kick-off with Newcastle United, Neville then focuses on the players and they certainly didn't emerge with any credit from the former Red Devils defender.
"I hope it's not true but, if it is true, it's an absolute disgrace".
"Who is qualified in that football club to be able to tell Jose Mourinho that Alderweireld, Maguire or Boateng are not better than the centre-backs they've got?"
When pushed on who is at fault for United's woes, a coy Mourinho replied: "The same people that were to blame with the fantastic season of last season".
The under-pressure Portuguese manager may agree with Merson's assessment of the Magpies' current attacking threat however it's clear that he wouldn't choose to play Benitez's side ahead of anyone, as it's a hard game. For example, Pogba is actually running further than ever before for the club.
While the Magpies boss' tactics may have not racked up the points, by adapting a defensive style when playing the so-called big sides in the league, he frustrates and forces them to play to their best to get any sort of a positive result.