Cameron said there were lots of the author's characters he would not like to be - and that the British public might see him as one of them.
He was asked to choose a Rowling character to emulate by a student at Kazakhstan's Nazarbayev University today.
Rowling's seven-book Harry Potter series saw sales in the hundreds of millions and gave rise to eight films.
Cameron, 46, said his nine-year-old daughter had just begun reading the books so he was now "rediscovering them".
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But he admitted the chances of UK voters seeing him as the forever youthful, popular hero were slim.
"I suspect people in Britain might want to paint me in a different role," he said. "But I'll let them do that. I won't make the work easier for them," BBC quoted Cameron as saying.
The prime minister did not elaborate on which other characters his domestic audience might like to cast him as.
Cameron is in Kazakhstan on a trade visit - the first serving British prime minister to visit the oil-rich nation.