The decision-making takes place next week at the WTO's own elegant headquarters on the shores of Lake Geneva where a formal "beauty parade" will be held to sort out leading runners for the role.
It is being hotly contested.
Nine senior global politicians have been nominated by their Governments leading up to the January 31 closing date. Six are men and three are women.
Over three days they will set out their vision for the WTO, come under strong questioning from trade ambassadors, then front the press at the end of the process.
Groser concedes it will take months to determine the successful candidate, "unless I fall out at the first stages".
If the role is determined on international political considerations alone he doesn't stand a hope as the only candidate nominated by a developed country. But Groser told this columnist he definitely stands a good chance if the job is determined by merit.
"There are other people of considerable merit standing for it but I definitely would compete." If it is done on the basis of practical experience and getting things done in the WTO - he considers he has an "excellent chance".
Groser is a previous chair of the WTO's agriculture negotiations.
Nine countries, including Ghana, Costa Rica, Kenya, Jordan, New Zealand, Mexico, Indonesia, South Korea and Brazil, put forth contestants to vie for the position.
The five WTO directors-general - including Pascal Lamy whose term expires on August 31, have been from Ireland, Italy, New Zealand, Thailand and France.
Given the predominance of developed-country appointees, the balance may well be tipped in favour of a nominee from a developing country.
Bloomberg has suggested three front-runners have already emerged - Ghana's Alan John Kwadwo Kyerematen, a former Minister of Trade and Industry, Anabel Gonzalez of Costa Rica, who is her country's current Trade Minister and previously ran the WTO's Agriculture and Commodities Division, and Groser.
The WTO acts as the global policeman for the rules-based international trading system as well as being a forum for negotiations.
Essentially the WTO's Doha Round has been in the deep-freeze since the global financial crisis.
But negotiations have proceeded on other fronts as the world's trading powers bypass the WTO to cement a vast number of bilateral and regional trade agreements.
Whether Groser does ultimately prevail or one of the other contestants, he or she has a tough job ahead.
WTO members also have to prepare for this December's upcoming ministerial conference in Bali, where a small package of deliverables from the long-running Doha Round of trade talks worked up under Lamy's leadership will be discussed.
If Groser does win the role, New Zealand will need a new Trade Minister.
Yesterday, John Key surprised the political pundits by dumping two ministers and pole-vaulting two younger MPs into Cabinet.
Kate Wilkinson did not try to hide the truth that she had been dumped. Heatley was a no show earlier in the day.
It makes sense putting Nick Smith into housing. This is a flash-point for the National-led Government.
Prices are going through the roof again and plans to make room for more housing in Auckland have been tepidly (to say the least) put into action.
Smith and Finance Minister Bill English should have little difficulty forming a flying wedge on this score.
Nikki Kaye's nose would have been out of joint if Simon Bridges had made the inner Cabinet ahead of her.
Kaye's experience as chair of Parliament's education select committee will provide some ballast to Education Minister Hekia Parata.
But sacking Wilkinson and Heatly - yet leaving the woeful under-performer Parata on the front-bench - will leave a sour taste among other MPs.
It smacks of "teacher's pet" or "too big to be allowed to fail".
