According to the New York Times, Mr Trump directed a Republican National Committee member from Illinois to pass on a threat to Mr Kinzinger, using a profanity, while they attended a fundraising event in Chicago.
Mr Trump asked Richard Porter, an RNC member from Illinois, whether or not Mr Kinzinger was running unchallenged, and after he had criticised the party’s then-presidential candidate.
The congressman had also publicly supported another presidential nominee, Jeb Bush, during the Republican primaries - in a stance that also appeared to anger Mr Trump.
Mr Porter, the RNC member, was allegedly told by Mr Trump to pass on a “vulgar message about what he [Mr Kinzinger] should do with himself,” and pressed his finger into the RNC member’s chest.
As the RNC member told the Times on Monday, when Mr Kinzinger was told about the then-presidential candidate’s comments, the Republican congressman reportedly "laughed and invited Mr Trump to do the same.”
Mr Kinzinger, a six-term Illinois Republican, has repeatedly spoken out against Mr Trump's conduct since his 2016 candidacy, when he said Mr Trump “was beginning to cross a lot of red lines of the unforgivable in politics,” as CNN and Politico reported at the time.
Although he largely supported Mr Trump’s policies while president, Mr Kinzinger was among eleven House Republicans who voted to impeach Mr Trump on 13 January following the attack on the Capitol by the former president’s supporters.
Mr Kinzinger’s interview with the Times came after his Republican colleagues in the Senate refused to convict Mr Trump for impeachment and inciting the 6 January Capitol riot on Saturday.
The congressman said the party needed to reckon with the former president and his allies in the Republican party, or continue to lose to Democrats and said: “We just fear. Fear the Democrats. Fear the future. Fear everything.”
“And it works for an election cycle or two. The problem is it does real damage to this democracy,” Mr Kinzinger told the Times. “We have a lot of work to do to restore the Republican Party, and to turn the tide on the personality politics.”
The congressman intends on running for re-election for his seat in 2022, despite criticism from other Republicans for his criticism of, and stance on, Mr Trump.