WASHINGTON—Former Obama White House counsel Greg Craig expects to be indicted in the coming days on charges stemming from work he performed for Ukraine in 2012, Mr. Craig’s legal team said.

Mr. Craig has refused to accept a plea deal, and the matter could be presented to a grand jury for indictment as soon as Thursday, people familiar with the matter say. A spokesman for the Justice Department declined to comment.

The people familiar with the situation say they believe Mr. Craig will be charged with making false statements to the Justice Department unit that oversees the activities of foreign agents, though other charges are possible.

An indictment of Mr. Craig is likely to send shock waves through the U.S. legal community and is the latest fallout from an investigation into former Trump campaign manager Paul Manafort and his years of work for the pro-Russia regime in power in Kiev.

The 74-year-old Mr. Craig is a legal heavyweight who served in senior legal roles for two Democratic presidents. He has also been a top State Department adviser and Capitol Hill aide.