The Brazilian has not lost in the 10 games he has started for the club but he has repeatedly risked his record with some reckless defending - and his manager fears it could get hairy for him at Old Trafford.
'He is an optimist positionally sometimes,' said Ancelotti. 'It is not for a defender to be an optimist.'
Optimist: But David Luiz should play more conservatively, according to his boss
Luiz has made a big impact at Chelsea and scored important goals, including one against United, but he has a dangerous habit of getting too tight to the striker he is marking.
He showed his hopeful side when he tried to steal the ball from Clint Dempsey and conceded a penalty on his debut at Fulham in February, and he made a similarly ill-judged challenge last month when Birmingham converted the spot-kick he gave away.
Neither proved costly in terms of the result, but these were not isolated incidents.
Foul play: David Luiz fouls Manchester United's Wayne Rooney
Most notably, Luiz got away with some dodgy challenges on Wayne Rooney and was lucky not to be sent off when Chelsea beat Manchester United at Stamford Bridge in March.
Rooney pulled the defender out of position time and again and beat him with his movement and United could also profit if Luiz roams upfield and out of position.
It is why Ancelotti is keen for the Brazilian to curb his enthusiasm. Denis Law: Sir Alex knows about winning with style but Mourinho's way is not for UnitedManchester United's 18 titles and counting. but can they beat Chelsea?Rampant Rooney could make it hairy for lucky LuizAll the latest Chelsea news, features and opinionAll the latest Manchester United news, features and opinion
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