WASHINGTON—The White House is reviewing a request by Russian President Vladimir Putin to allow Russian investigators to question a number of Americans they say are implicated in criminal activity, including a former U.S. ambassador, a spokeswoman said.

The White House decision to weigh the proposal rather than dismiss it outright prompted alarm among former diplomats and on Capitol Hill.

White House press secretary Sarah Sanders confirmed Wednesday that Mr. Putin and President Donald Trump discussed a desire by Russian authorities to question a number of U.S. citizens, including Michael McFaul, a former ambassador to Russia under President Barack Obama who now lectures at Stanford University.

Asked at Wednesday’s daily briefing whether Mr. Trump was “open to having U.S. officials questioned by Russia” including Mr. McFaul, Ms. Sanders replied, “There was some conversation about it but there wasn’t a commitment made on behalf of the United States. The president will work with his team, and we’ll let you know if there’s an announcement on that front.”

As ambassador, Mr. McFaul was an architect of Mr. Obama’s attempted reset with Moscow, but was sometimes critical of the Kremlin, a posture which brought intrusive Russian media scrutiny and official accusations that his mission was to undermine the country’s leadership.