Cole has been accused of cheating on his wife Cheryl while Terry remains in the spotlight for his affair with Wayne Bridge's former girlfriend Vanessa Perroncel.
But while England boss Fabio Capello sacked Terry as captain of the national team, Ancelotti does not appear ready to take a hard line against his wayward stars.
Focus: Ashley Cole (right) and John Terry dispossess Inter Milan's Mario Balotelli in a pre-season friendly
'I don't care who my captain or troops go to bed with, but what ideas they wake up with in the morning,' was Ancelotti's abrupt response when questioned about claims that Cole sent naked photographs of himself to topless model Sonia Wild.
Allegations: Ashley (right) has been accused of cheating on his wife, Cheryl
The 29-year-old denied he was responsible for the text messages, but has been hit by further allegations that he slept with another woman at the Chelsea team hotel before two Barclays Premier League games.
Cole has the benefit of being out of the limelight for the next three months after picking up an ankle injury, giving his boss a headache ahead of the Champions League clash against Inter Milan on Wednesday week.
The former AC Milan boss spent much of the last two seasons sparring with Inter counterpart Jose Mourinho, but insists he greatly respects the self-styled 'Special One'.
'We're level,' Ancelotti told La Stampa. 'In the derby last year, we won 1-0 in the first leg and it was 2-1 to him in the return.
'Jose is a great coach who I respect a lot. I know what he has given to Inter and I know what he left Chelsea: even the coat that is in the club's museum. But the match won't be about us. It will be about the players.'
Ideas: Ancelotti (right) is only concerned about how his players perform on the pitch
Reunited: John Terry and wife Toni smile for the cameras at Heathrow Airport
Ancelotti is not prepared to put his chances of success against Inter at more than50-50, admitting that much of his side was built by the Portuguese.
The Italian sees similarity between the two sides in the way they marry physical strength with quality, singling out Diego Milito, Samuel Eto's and particularly Wesley Sneijder as threats to his side.
That said, he insists the Blues have moved on, even from the side that grew last season under Guus Hiddink.
'There is more thunder, we play with more movement,' he said, describing Nicolas Anelka as his playmaker.
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