The Old Trafford club are now 11 points adrift of fourth-placed Chelsea after losing 3-1 to bitter rivals Liverpool on Sunday and Mourinho is facing questions about his future.
Approaching the midway point of the season, it would be an incredible turnaround from the Portuguese boss to reinvigorate his fractured squad and outpoint two of the Big Six.
The 20-time league champions looked bereft of ideas to overcome table-toppers Liverpool, against whom they have maintained a good record in recent years.
Jurgen Klopp’s men showed the gulf between the two sides in their ball retention (64.5 per cent possession) and productivity (36 shots, of which 11 were on target).
In a frosty post-match interview on Sky Sports, Mourinho refuted suggestions that he could not lead his side to a Champions League spot.
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“We can still finish fourth. It’s not easy,” he said.
“For sure, for sure, we’re going to finish in the top six like historically all the top teams.
“We can get the fourth position. Now we have to look to the fifth, and probably later the fourth.”
Former Gunners midfielder Parlour, who won three Premier League titles at Highbury, wholly disagrees with The Special One, however.
He told talkSPORT: “Jose was saying after the game they’ve still got every chance of getting in the top four, but I can’t believe he said that.
“I don’t think they’ve got any chance. I just don’t think they’re good enough.
“The recruitment has got to be better and at the moment I just don’t know where Man United are going.
“They’re so far away from teams like Liverpool and Manchester City, and you could even put Chelsea and Tottenham in there.
“I just can’t see them coming anywhere near the top four.”