The newspaper said that one phone call between the president and the Kentucky Republican devolved into a "profane shouting match."
Relations between the two men have been conspicuously tense. Trump has repeatedly slammed McConnell on Twitter, blaming him for the failure of the GOP's attempts to repeal and replace the Affordable Care Act.
But the Times reports that the strained relationship between McConnell and Trump is even more apparent in private. The newspaper said that McConnell has bristled at the president's attacks on his Senate colleagues. The career politician has privately expressed doubts about Trump's ability to lead the GOP, the Times reported, citing people who have spoken directly to McConnell.