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Featured Image Credit: Alamy
Rudiger, 29, joined Madrid on a free transfer earlier this summer after coming to the end of his contract at Stamford Bridge.
He made his debut for the European champions on Saturday as they were beaten 1-0 by rivals Barcelona in an ill-tempered pre-season match in Las Vegas.
Rudiger unexpectedly started at left-back as Ancelotti opted to stick with David Alaba and Eder Militao in central defence, the same centre-back pairing that won his side both the Champions League and La Liga last season.
Germany international Rudiger looked comfortable at full-back but it was his opposing player, former Leeds winger Raphinha, that scored the only goal of the match to secure victory for Barcelona.
Nevertheless, Ancelotti was pleased with the performance of Rudiger, who was brought off at half-time as one of six changes for Madrid at the interval.
"I liked him a lot. I am not crazy and he is very intelligent," said Ancelotti, explaining his decision to play Rudiger at left-back.
"He can play in that position, just as he can also change in the match with Alaba.
"They didn't do so today, because it went well. [Alaba] as a left-back... only when necessary.
"I don't want to change the pair from last year."
The position is not completely unfamiliar for Rudiger, who was used to playing on the left-hand side of a back three during his time at Chelsea.
The versatile defender has also filled in a right-back for both Chelsea and the German national team.
Rudiger could make his second appearance for Madrid when they take on Mexican side Club America in San Francisco on Wednesday.
Ancelotti's side will then face Juventus in Pasadena on July 31 before taking on Europa League winners Eintracht Frankfurt for the UEFA Super Cup on August 10.
Madrid will then begin the defence of their La Liga title away at Almeria on August 14.