David Cameron is prepared to back Peter Mandelson for a major international job as the next director general of the World Trade Organisation, raising the prospect of a fourth comeback by the man once known as the Prince of Darkness.

In a sign of the prime minister's high regard for Labour's last business secretary, government sources indicated that Mandelson was seen in Downing Street as a strong candidate to succeed Pascal Lamy, who is to stand down as the WTO director general next year.

"Peter Mandelson is a strong candidate for an international job," one government source said of Britain's former European trade commissioner. "The director general of the WTO, which will become available next year, is an obvious position. We are sure that Peter Mandelson would have a lot to offer."

The interest in Mandelson may be seen in Labour circles as troublemaking by the coalition, which is rubbishing Gordon Brown's unofficial campaign to fill the vacant position of managing director of the International Monetary Fund after the resignation of Dominique Strauss-Kahn. The former prime minister made a speech in South Africa calling on rich western countries to meet their pledges to fund education for the world's poor.

Mandelson has been ruled out by Britain as a possible IMF head because he is does not have the necessary qualifications as a former finance minister or a former central bank governor. "Peter Mandelson does not have enough credibility for the IMF," the government source said.

But the government does believe he would be well placed to succeed Lamy, Mandelson's French predecessor as EU trade commissioner. Lamy is a highly respected figure, though Cameron has been highly critical of the WTO's failure to complete the Doha trade round.

One government source laughed off Brown's campaign. "What a clever idea to launch a campaign for the IMF with a speech calling for action in an area that is the responsibility of the World Bank. Bob Zoellick [the US president of the World Bank] will be really impressed. The IMF is rather more focused on keeping the world financial system afloat."

Government sources believe they will not need to lobby against Brown during next week's state visit to Britain by Barack Obama and at the G8 summit in France on Thursday and Friday because the former prime minister enjoys negligible support.

One government source said: "Gordon Brown hasn't even bothered to make contact with us. We do not need to say what we think – even if we threw our weight behind him he would not stand a hope in hell. It is all a bit sad."

Britain is expected to agree with Wolfgang Schäuble, the German finance minister, who has called for the EU to agree on a candidate from a eurozone member. The EU, which has traditionally provided a candidate to run the IMF while a US figure runs the World Bank, controls 32.07% of the IMF voting rights.

Christine Lagarde, the French finance minister, is the current eurozone frontrunner. But Britain expects that a strong German candidate, possibly the former Bundesbank governor Axel Weber, could emerge.