President Trump has used services of the New York lawyer – known as a tenacious litigator – for more than a decade.
Last week, former FBI boss Robert Mueller was named special counsel for the Department of Justice inquiry.
Donald Trump denies any collusion between his campaign and Russia.
However, US intelligence agencies believe Russia tried to tip the 2016 election in favor of Donald Trump.
Marc Kasowitz and the White House have so far made no public comments on the reported appointment.
He is well known to Donald Trump, and it was he who – during the presidential campaign – threatened to sue the New York Times if it didn’t retract a story about Donald Trump touching women inappropriately.
The New York Times stood by its story and a retraction was never published.
Calls for a special investigation had mounted since President Trump fired the most recent FBI director, James Comey, earlier this month.
The FBI and Congress are also looking into potential links between Donald Trump’s campaign team and Russia.
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