The Red Devils suffered a surprise 3-2 loss to Brighton and Hove Albion in their second Premier League fixture of the season.
Manchester United slumped to successive losses at Brighton to heap pressure Jose Mourinho at the start of the Premier League campaign.
The 20-time English champions are three points adrift of title holders Manchester City to lose vital ground at the start of the season.
Mourinho has a reputation for losing his way in his third campaign at his previous clubs to fuel media speculation that the Portuguese coach could soon be on his way.
Manchester United will take on Tottenham Hotspur at Old Trafford in their next Premier League clash on Monday night in what promises to be a difficult assignment.
Former Manchester United winger Sharpe suggested that Mourinho could be sacked before Christmas if the Red Devils’ poor form continues.
“(Mourinho) is the wrong man for the job,” Sharpe told the Daily Mail.
“When he came to Chelsea the first time he was quite charming and fun, but now he just seems dour and fed up.
“He’s moaned about not signing new players and not bigging up the ones he’s got.
“The football’s not entertaining and what makes it twice as bad is that their two biggest rivals, Man City and Liverpool, do play exciting football.
“His negative style does not fit in with the expansive football that United fans want. I think he’ll be gone before Christmas.”
Manchester United haven’t won the Premier League title since 2013 when Sir Alex Ferguson led the Red Devils to their 13th top flight crown under his management.
The Red Devils finished Mourinho’s second season without a trophy following a 1-0 loss to Chelsea FC in the FA Cup final at Wembley.
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