Brazil believes it has the best person for that near-impossible task in Roberto Azevedo, its permanent representative at the WTO in Geneva since 2008 who has participated, in some form, in nearly all WTO ministerial conferences since the launch of the Doha round.
Azevedo is competing for the job with eight other candidates, from Ghana, Kenya, Costa Rica, Indonesia, New Zealand, Jordan, Mexico and South Korea.
He visited South Africa recently on a whirlwind African tour, sometimes touching down in two countries in a day, to present his case, meeting Trade and Industry Minister Rob Davies and director-general of International Relations and Co-operation Jerry Matjila.
As Azevedo and Brazil present it, the next WTO boss will have to be a skilled trade negotiator, capable of rising above his national and regional affiliations and impartially representing the interests of all countries – yet someone who at the same time is "representative and legitimate".
And the latter means, at this moment, someone from a developing country, Azevedo said in an interview, because "there is a tacit understanding that this is the turn of the developing countries. It is not by accident only one candidate, New Zealand's, is from the developed countries." But he is quick to stress that taking into account representivity and legitimacy need not compromise the quality of the next director-general as "there are excellent candidates in both camps".
Yet in a field which includes eight candidates from developing countries, it is the quality of the individual which is likely to count most, and that is what he is clearly stressing in his election campaign, which he says is going as well as expected. On the continuum from "downright catastrophic" to "it's in the bag", he believes he's "closer to the optimistic side".
He seems to be counting most on support from own continent, South America, as well as the nearby Caribbean and Central America but also from Africa. And he thinks his campaign is also in "good shape" in Europe and the rest of the developed world too, though he still had much canvassing to do.
The selection will take place by the end of May.
Azevedo said his counterparts from other countries at the WTO in Geneva know him from his performance at the negotiation table as a capable and helpful negotiator, independent of his nation's interest, who, if chosen as the next director-general, would work for a global trade deal that is fair to all.
For example, he dismisses any suggestion that he should be seen as the candidate of the Brics nations (Brazil, Russia, India, China and South Africa).
But from the great distances of the capitals of the world, he and other candidates are more likely to be seen as representing the narrow interests of their nations or regions and so he is touring the capitals to correct any such misconceptions.
To anyone who doubts that it is possible for a director-general to transcend his nation's interests, he points to the impartial and constructive way the current incumbent Lamy, a Frenchman, lead the WTO's agricultural negotiations, despite this being an area very sensitive to France.
That, he adds, is the problem all candidates have to deal with.
He acknowledges, in effect, that the most important criterion in choosing a new WTO boss will be who can unlock the Doha round which deadlocked mainly because the developed and developing worlds couldn’t reach a compromise on opening each other's markets.
But he casts the problem wider.
"The question is not so much what you do about the Doha Round, but what you do to advance the system, to make the system evolve. But to do that, one must solve the Doha Round. I don't think you can abandon it. I don’t even think that you can abandon the mandates."
He believes that it's possible to do a lot of things to solve the key issues in the Doha Round. But how?
"The bad news is that the gaps between negotiating parties are extremely large. And I don't think they will be closed. Not in the way we have been formulating things. The good news is that we have only a few areas of negotiations where we have those gaps. So if we solve those, then the whole round moves. And it moves quickly I think. So we have to attribute priority to those areas."
Negotiators must consider what they can do rather than what they would like to do, he stressed. The danger was that if the negotiations began anew, negotiators would quickly retreat to old expectations, and old negotiating benchmarks.
So the negotiators would have to take new roads if they wanted to make progress. Azevedo said he believed that the world had changed considerably since the negotiations broke down, not least because of the global crisis and suggested this had lowered expectations which could help move the negotiations.
Another positive factor is that he had discovered all WTO members wanted a deal, because they realised that what was at stake was not just the Doha Round but the future and credibility of the trade system as a whole. Those two factors were very strong building blocks on which to build a fresh approach.
It was important to go back to constituencies and try to convince them that a win-win solution was possible as negotiators had not talked to their constituencies for a long time. Some basic concepts had emerged from his discussions about that fresh approach but to expose them prematurely would jeopardise them. He believed he was the one to do the unlocking of the Doha talks because he was already well known to his fellow-negotiators in Geneva and capable of winning their trust quickly. And that was important because the next director-general had to "hit the ground running".
Azevedo was meeting the South African government because South Africa was "a very important player, not only in terms of the quality of its contribution in Geneva but because of its leadership role in the region and in the WTO".