The US president has warned Mr McConnell he will step up attacks on senators who criticise him unless they fall in line, according to CNN.
A string of Republicans have spoken out against or refused to defend Mr Trump’s apparent attempts to pressure foreign governments into helping his election campaign.
Mr Trump demands total loyalty from those within his party and frequently lashes out at critics on Twitter.
On Saturday he called senator Mitt Romney as a “pompous ass” after the former presidential candidate said Mr Trump’s “brazen and unprecedented” appeal to Ukraine and China to investigate Joe Biden was “wrong and appalling”.
In private, the president is said to be leaning on Mr McConnell to ensure loyalty among GOP senators in a return to the kind of anxious behaviour he exhibited at the height of Robert Mueller’s Russia investigation.
The Senate majority leader has told “a small number of Republicans” about Mr Trump’s frequent calls, reported CNN, which cited an anonymous person familiar with the conservations.
Doug Andres, Mr McConnell’s press secretary, dismissed the report as “categorically false”.
“Leader McConnell never said anything like this," he added.
The Senate majority leader is facing with attempting to preserve unity among Republicans while also placating an erratic president who has been tweeting furiously about the Democrats' impeachment probe.
The Democratic-led House of Representatives is pushing forward with the inquiry over Mr Trump's call to the Ukrainian president despite the White House's refusal to co-operate.
The three congressional committees leading the inquiry were this week working on final arrangements to interview a US intelligence officer who filed the whistleblower complaint that triggered the probe.
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