The Red Devils have failed to win their last four games in all competitions to heap pressure on the Portuguese head coach.
Manchester United returned from the international break and produced a stodgy performance in a 1-1 draw with Wolves at Old Trafford.
The 20-time English champions suffered a loss to Frank Lampard’s Derby County side on penalties in the Carabo Cup third round.
Mourinho’s men slumped to a 3-1 loss to West Ham United at the London Stadium on Saturday evening to tumble down to tenth place.
Even the inclusion of Alexis Sanchez couldn’t inspire Manchester United to a much-needed win over Valencia in the Champions League.
The Red Devils were held to a 0-0 draw with the Spanish outfit at Old Trafford to leave Manchester United winless in four outings.
Mourinho has reportedly fallen out with a number of key Manchester United stars this season, including Paul Pogba and Antonio Valencia.
Former Arsenal star Keown believes Mourinho could be facing a decisive game in his future at Manchester United.
“I don’t believe he can — especially if he loses the fans,” Keown told the Daily Mail.
“The Manchester United faithful have been incredibly patient with their team. So far, Mourinho has not lost them.
“The players are playing with fear. Is it any wonder their confidence is looking brittle if their manager is ranting for 45 minutes before an important match?
“That could go some way to explaining why United looked devoid of confidence against Valencia.
“As a former player, I would love to pull on my boots and play for Jurgen Klopp or Pep Guardiola. With these managers, you feel they are taking every step with their players. They nurture their players and only have their best interests at heart.
“With Mourinho, it feels like the players are on their own. It is like they are always on trial. It must be a lonely road for them at United.”
Manchester United finished in second spot in the Premier League table last term, but their position was deceiving given the Red Devils ended up 19 points adrift of Premier League champions Manchester City.
The 20-time English champions have already lost three Premier League games this season, suffering defeats by Brighton and Hove Albion, Tottenham Hotspur and West Ham.
Mourinho took over the reins from Louis van Gaal in May 2016 and the Portuguese head coach was charged with restoring the Red Devils to the pinnacle of English football again.
Manchester United haven’t won the Premier League title since 2013 when Sir Alex Ferguson was still in charge of the Red Devils.
The Red Devils have only managed to finish in the top four on three occasions in the past five seasons since the Scottish head coach stood down.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news