The Washington Post reports that Mr Trump made the call on 23 December as the investigations chief for the Georgia secretary of state’s office pursued allegations of ballot fraud in the suburbs of Atlanta.
Citing people familiar with the call, the Post says that Mr Trump allegedly told the official they would be a “national hero” if they found evidence of fraud.
The president has made at least three separate calls to state officials in Georgia seeking to overturn or complaining about the results of November’s presidential election.
In this instance, Secretary of State Brad Raffensperger had launched an investigation to determine if election officials in Cobb County had accepted mail-in ballots that did not match those on file. Mr Trump’s call came as inquiries were underway.
The allegations were eventually determined to have no merit.
Mr Raffensperger confirmed to the Post that Mr Trump made the call in December but was not aware of the details of what was discussed — though he did say it was inappropriate for the president to attempt to intervene in an investigation.
The first known incidence of Mr Trump speaking with officials in Georgia regarding the election was in early December when he criticised Republican Governor Brian Kemp for certifying the state’s election results.
On a 2 January call the president both threatened and flattered Mr Raffensperger in an attempt to get him to overturn the election results.
Audio of the conversation was made public. Mr Trump says to the secretary of state: “Go find me some votes.”
Legal experts have flagged the call as a possible violation of state or federal law.
The Post’s source says that the 23 December call was similar to that made to Mr Raffensperger.
No evidence of widespread voter fraud was found in Georgia or any other state.
President-elect Joe Biden became the first Democrat to win Georgia since 1992 with 49.5 per cent of the vote with a count of 2,473,633 ballots.
Mr Trump lost Georgia by 11,779 votes.
The Independent has contacted the White House for comment.