Veteran Washington lawyer Emmet Flood is under consideration for a White House job assisting U.S. President Donald Trump with the Russia probe, according to a person familiar with the matter.

Flood, who advised former President Bill Clinton in impeachment proceedings, met with Trump in the White House this past week, the person said, but no decision about the job has been made.

The discussions were first reported by The New York Times, and on Sunday morning Trump tweeted that the Times had written a "false story" that he was unhappy with his legal team and would add another attorney to help out.