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.

Mr. Sondland is co-founder and chief executive officer of Provenance Hotel Partners. Neither he nor the White House was immediately available for comment. The State Department referred an inquiry to the White House.

Through associated companies, he donated $1 million to Mr. Trump’s inaugural committee, according to Federal Election Commission records.

However, he wasn’t always a supporter of Donald Trump. During the GOP primary race preceding the 2016 presidential election, Mr. Sondland made the maximum contribution allowed by law to Jeb Bush and put $25,000 into an outside group supporting the former Florida governor, records show.