The Prime Minister revealed the unlikely aspiration during a question and answer session with students in which he also opened his heart about missing wife Samantha "desperately".
He also told students at the Nazarbayev University in Kazakhstan's capital Astana that he still gets told off by his former Oxford tutors for mistakes in running the country.
Asked which character in the JK Rowling books he would like to be, he said: "My daughter is nine years old, she's just started to read all the Harry Potter books so I'm sort of rediscovering them all over again.
"I can think of all sorts of characters you don't want to be and I suppose in the end you know if you've got any sense you want to be Harry Potter. That must be the correct answer.
"But I suspect people in Britain might want to paint me in a different role but I'll let them do that, I won't make the work easier for them."
Cameron, who has been overseas since Thursday on a visit taking in the European Council in Brussels, Afghanistan, Pakistan and Kazakhstan, said he was missing his wife.
Asked what moment of his life he would like to relive, the Prime Minister said: "I do still remember vividly the day I was married. It's the most exciting day of your life. I still remember it.
"I haven't seen my wife for several days now and I miss her desperately. That would be my answer."
He added: "Of course the birth of your first child, particularly is an incredibly emotional and powerful moment."
Asked about his student days reading politics, philosophy and economics at Oxford, Cameron said: "I was very lucky to have some very good tutors.
"In fact some of them still write me letters, often telling me that what I am doing is not a good idea but every now and again saying well done.
"They keep in touch, I think they still feel they are training me even now."
Cameron was presented with a Nazarbayev University hoodie and cap on his visit.