Mr Azevêdo admitted the WTO "has to change" and be "reformed" amid mounting pressure for tougher rules on 'developing' countries such as China.
The WTO had been "very unfair" to the US and was used by China as a "vehicle" for its explosive growth, Mr Trump said just before leaving Davos.
"We are talking about a whole new structure for the deal, or we will have to do something," he said. "We are going to do something that will be very dramatic. He [Azevêdo] will be coming with a lot of his representatives to Washington sometime next week or the week after and we will start working on it."
The WTO has been criticised for its inability to stop countries using state aid and underhand tactics, such as steel dumping, to gain an advantage over rivals in the international trade system.
Some developing countries are given more leeway though so-called special rights.
The US, EU and Japan issued a joint statement on Tuesday calling for the WTO to enact more strict rules to stop Chinese companies benefiting from state support.
- Telegraph