The Post further notes that former Trump campaign chair Paul Manafort, who helped Yanukovych's 2010 campaign, "eventually admitted that he and other lobbyists used the Skadden report as part of a broad effort to improve Yanukovych's reputation in the West, which had suffered after the widely condemned jailing of Tymoshenko".
"Mr Craig is not guilty of any charge", they said.
In a statement to the Journal, Craig's lawyers said the case has been investigated and should be put to rest.
The case against Craig stemmed from Special Counsel Robert Mueller's Russia probe, centering around the lobbying work he performed in 2012 for the Russian-backed president of Ukraine, Viktor Yanukovych, while Craig was a partner at the law firm Skadden, Arps, Slate, Meagher & Flom.
Craig resigned from Skadden in April 2018 amid a building investigation into whether the firm's lawyers didn't register as foreign lobbyists for their Ukraine engagement.
Craig's lawyers did not say why they expect him to be charged.
The White House and Justice Department did not immediately respond to a request for comment from The Hill.
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"We expect an indictment by the DC US Attorney's Office at the request of the (Justice Department's) National Security Division", Craig's lawyers William Taylor and William Murphy said in a statement.
The apparent lobbying work was done after Craig's tenure as White House counsel, according to the report. John Edwards and James Cartwright, the former vice chairman of the Joint Chiefs of Staff, who was charged in a leaks investigation. CNN has reported that the statute of limitations for the matter for which Craig was originally investigated - having failed to register as a foreign agent - has expired and that prosecutors have instead been weighing bringing a false statement charge against him.
Investigators have focused in on whether Craig made false statements to the department regarding registration as a foreign agent, the Post reported.
CNN reported last month that the Justice Department has been exploring a FARA case against Craig for so long that the statute of limitations on the original alleged offense had expired.
They said he spoke to reporters at The New York Times about the report to "make certain that the Times would accurately summarize the report's criticisms of the Tymoshenko trial and not rely on misinformation from Ukraine and its representatives".
Craig went to Yale Law School and was a classmate of former President Bill Clinton and Hillary Rodham.