Mourinho is under pressure after Sunday's dismal 3-2 defeat at Brighton & Hove Albion.
"He is the wrong man for the job," Sharpe told Press Association Sport.
“When he came to Chelsea the first time he was quite charming and fun, but now he just seems dour and fed up.
"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."