President Trump's recent feud with Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGraham: GOP will confirm Trump's Supreme Court nominee before the election Trump puts Supreme Court fight at center of Ohio rally The Memo: Dems face balancing act on SCOTUS fight MORE (R-Ky.) could dampen the president's enthusiasm for backing McConnell's pick in the Alabama special Senate primary, according to a new report on Friday.

Trump backed Sen. Luther Strange (R-Ala.) after a push from McConnell and others who wanted a unified GOP front.

Strange was appointed to temporarily fill the seat in February when former Sen. Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE (R-Ala.) became attorney general.

The Washington Post reported that Trump has not expressed an interest in withdrawing his endorsement of Strange. However, he is reportedly debating whether to take a more hands-off approach to next month's primary runoff.

A source close to Strange's campaign denied the report.

"Sen. Strange spoke with both President Trump and Vice President Pence today, during which they reiterated their support and discussed potential events to show that support," the source said.

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Ahead of the August primary, Trump tweeted support for Strange on a handful of occasions and recorded a robocall in the state on his behalf.

But now aides are reportedly counseling Trump not to mention Strange and the Post adds that there are no current plans for Trump to travel to Alabama to stump on Strange's behalf.

Strange finds himself in the race falling behind former Alabama state Supreme Court Chief Justice Roy Moore, a controversial figure who has a strong cadre of supporters among the state's conservative base of voters. Most recent polls put Strange behind by as much as double digits, although one commissioned by the pro-Strange Senate Leadership Fund found Strange only four points behind.

Winning Trump's support was a boon for Strange in a state where Trump is still beloved by Republican voters. The race has turned into a battle over who can hug Trump tighter, so the endorsement had insulated Strange against Moore's claims that he would be the better candidate to carry Trump's torch in the Senate.

The Post frames the potential cooling-off as a result of the frayed relationship between the president and the Senate majority leader. Trump has needled McConnell on Twitter this month for failing to deliver a successful vote on healthcare.

Meanwhile, a recent report from The New York Times said McConnell is privately questioning whether Trump can rebound from a string of controversies to turn his agenda around.

McConnell and those close to him vastly prefer Strange to the more controversial and unpredictable Moore, who has blasted McConnell as a member of the Washington establishment "swamp." There's also concern that Moore might not be as reliable as a vote for GOP leaders when they look to shepherd through legislation with a slim, two-vote majority.

Trump has been willing to play ball by backing leadership's picks in special elections this year, but if Strange can't pull ahead, he could deliver Trump his first loss.

- This report was updated at 7:06 p.m.