Dubke, 47, who had been tasked with helping to shape the president's message, only served at his administration post for about three months.
Press secretary Sean Spicer is briefing reporters on Tuesday following President Trump's first trip overseas.
Dubke's last day may be as early as Tuesday.
Dubke previously was a Republican strategist who founded Crossroads Media and had long ties to party establishment figures, including strategist Karl Rove.
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Dubke was the rare Trump newcomer in a White House in which personal relationships and proximity to the president is the currency.
"Russian officials must be laughing at the United States & how a lame excuse for why the Dems lost the election has taken over the Fake News", he added Tuesday. His appointment came with some criticism, as CNN reported at the time that some inside the White House said they would have preferred a veteran from the campaign. Reports have circulated that Trump may bring in trusted former aides, including his original campaign manager Corey Lewandowski and former deputy campaign manager David Bossie, as the White House struggles to keep focused on its policy agenda while dealing with FBI and congressional investigations into possible Trump campaign ties to Russian Federation.
Dubke was a late addition to Trump's administration, replacing Jason Miller, who served in Trump's presidential campaign. Just back from his nine-day trip to the Middle East and Europe, Trump dismissed recent reports as "fake news". Shortly after the election, Kushner allegedly discussed setting up a secret communications channel with the Russian government to facilitate sensitive discussions about the conflict in Syria.
Trump tweeted Tuesday that "we have a MASSIVE trade deficit with Germany, plus they pay FAR LESS than they should on North Atlantic Treaty Organisation & military".
Trump has also been in talks with former campaign aides Corey Lewandowski and David Bossie about taking on more formal roles, possibly in a crisis management function.