Observers in Singapore at the weekend reported obvious tension between the pair in the wake of the Liberty Media buyout and American Carey's appointment as chairman.
Ecclestone is said to be staying as chief executive for three more years, but when asked about that by Sky Sports News he answered: "Let's see. We'll see."
One interpretation is that Carey will play the role of apprentice for a time before fully taking over, but the 21st Century Fox executive told F1's official website: "I am a bit too old to be an apprentice."
The opening salvos of the Liberty Media era have been obvious, with 85-year-old Ecclestone clearly unhappy.
Told that he has to work with Carey, he insisted: "The only thing I have to do is die and pay my tax. Short of that I don't have to do anything."
However, Carey is still hinting that the Ecclestone era is over.
"Sure, [running F1] is not a task for a committee, as committees tend to become bureaucratic, but there also can't be a dictatorship - even if probably here they are used to it," he said in Singapore.
Carey also said: "Certainly Hollywood is good training for dealing with unique personalities.
"With all credit to Bernie, he's had enormous success - the world admires Bernie for the business that he has built. But I still think that there is another level that we can take Formula 1 to."
Meanwhile, Mercedes's Toto Wolff will not be stepping in to replace Ecclestone as chief executive.
"I will not do it," he is quoted as saying by Osterreich, standing with fellow Mercedes chief Niki Lauda. "We both work together here and we want to keep working together here."
The season continues next weekend with the Malaysian Grand Prix.