WASHINGTON — Lawyers for Gregory B. Craig, a White House counsel in the Obama administration, expect him to be indicted in the coming days on charges related to his work for the Russia-aligned government of Ukraine.

The case against Mr. Craig, 74, stemmed from an investigation initiated by the office of the special counsel, Robert S. Mueller III.

An Ivy League-educated lawyer who held prominent positions in the Clinton and Obama administrations, Mr. Craig would become the first person who made his name in Democratic Party politics to be charged in a case linked to the special counsel’s investigation.

Mr. Craig would also become the first person to be charged in a case connected to the special counsel after Mr. Mueller finished his investigation into the 2016 presidential election. In a summary of the inquiry, Attorney General William P. Barr said that the special counsel’s team had concluded that there was no evidence that President Trump or his aides “conspired or coordinated with the Russian government in its election interference activities.”