The Portuguese coach has come under fire following the team's Champions League exit on Tuesday night.
The Red Devils were comfortably beaten 2-1 by Sevilla in the second leg of their last-16 clash following their failure to nab an away goal in their stalemate in the first leg.
Cundy has suggested that even though Mourinho guided United to Europa League and EFL Cup glory last season, the ex-Chelsea boss could be staring an the exit door soon.
"This is the beginning of the end for Jose at Old Trafford," Cundy told talkSPORT. "You'll go back to this result in years to come and say this was the beginning of the end.
"He's been there for two years, he's been brought in to win the Premier League and the Champions League and he's not got close. This year they had one of the easiest ties in the group for any English side and they had to get through out of the last-16 against Sevilla.
"This is catastrophic for Jose, it's one of the worst results in his career."
United's only chance of winning silverware this season is if they go all the way in the FA Cup.