WASHINGTON—As concern among some of President Trump’s top national-security advisers grew over his interactions with Ukraine, they confided repeatedly in an official whose role impeachment investigators are now examining: John Eisenberg.

Mr. Eisenberg, the general counsel for the National Security Council, fielded NSC officials’ complaints over efforts by U.S. ambassador to the European Union Gordon Sondland and Mr. Trump’s personal attorney, Rudy Giuliani, to persuade Ukraine’s President Volodymyr Zelensky to investigate Democratic presidential candidate Joe Biden as well as alleged Ukrainian interference in the 2016 election.

Some witnesses in the House impeachment inquiry cited orders from former national-security adviser John Bolton to report to Mr. Eisenberg the “drug deal,” as Mr. Bolton allegedly called it, that Messrs. Sondland and Giuliani were involved in. Mr. Bolton didn’t personally raise his concerns over Mr. Sondland’s activities with Mr. Eisenberg, a person familiar with the NSC general counsel’s thinking said.

Officials have testified that they believed both men were trying to persuade Ukrainian officials to investigate Mr. Biden and his son in exchange for a Trump-Zelensky meeting and the release of U.S. military aid that the White House had delayed. Mr. Trump has denied that there was any such quid pro quo.

It isn’t known publicly what, if anything, Mr. Eisenberg did with those reported complaints, and his handling of them is now a subject of debate.