Hogan laid out his strategy in a letter on April 30 to US Trade Representative Robert Lighthizer, Trump's point man in carrying out protectionist trade wars with Europe and China. "I believe that the current crisis presents a political opportunity to address these issues, and would be happy to hear if you agree," Hogan said in the letter, seen by AFP.
A European source said Hogan and Lighthizer had held an initial phone conversation on Monday that had gone positively.
The EU commission handles all trade negotiations for the EU 27 and represents the member states at the WTO.
EU-US trade relations have deteriorated since Trump came to power more than three years ago on a promise to close his country's yawning trade deficit with the rest of the world.
The skirmishes with Europe began when Trump imposed tariffs on steel and aluminium imports from the EU. Brussels shot back by taxing iconic US products, including denim jeans and motorcycles.
Trump has also threatened duties on European cars, which is of particular concern to Germany, but he has so far backed down under the pressure from US lawmakers.