Discussing the possibility of Brown as the next IMF chief on BBC, Cameron said someone who "didn't know we had a debt problem in the UK" might not be the best person to run the IMF.
The IMF, he said, should be led by someone 'extraordinarily competent', and suggested that the next IMF head could come from "another part of the world", such as China or India.
IMF chief are by convention from European countries - the current head is France's Dominique Strauss Kahn.
The UK and other major economies have an effective veto on the appointment, the BBC reported. Strauss Kahn is scheduled to step down soon as managing director of the IMF.
Cameron told the BBC Radio: "I haven't spent a huge amount of time thinking about this. It does seem to me that if you have someone who didn't think we had a debt problem in the UK... they might not be the best person to [run the IMF]".
He said: "Above all what matters is the person running the IMF someone who understands the dangers of excessive debt, excessive deficit, and it really must be someone who gets that rather than someone who says that they don't see a problem."
Cameron also said: "I certainly don't want a washed-up politician from another country. It's important that the IMF is led by someone extraordinarily competent."
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