BRUSSELS—Amid escalating tensions between the U.S. and Europe over trade and foreign policy, the Trump administration is moving to fill the long-vacant post of U.S. ambassador to the European Union.

Washington has asked the EU if Portland hotelier Gordon Sondland would be an acceptable nominee, according to two senior European officials. If nominated and approved by the Senate, a process that can take months, he would fill a job that has been vacant since January 2016.

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