According to the source, Rogers rebuffed the president's request, deeming it inappropriate. The encounter between Rogers and Trump was documented in a contemporaneous memo.
The White House told ABC News in response to the story that it "does not confirm or deny unsubstantiated claims based on illegal leaks from anonymous individuals. The president will continue to focus on his agenda that he was elected to pursue by the American people."
Trump’s request to Rogers is not the first time he has made such an appeal to a top intelligence official.
Following Trump's firing of James Comey on May 9, it was revealed that the former FBI director reportedly wrote a memo detailing a request Trump made to him in February to drop the FBI’s investigation of National Security Adviser Mike Flynn.
Rogers later testified in front of the House Armed Services Committee but was not asked about the report.
Asked about the report when he appeared today before the Senate Armed Services Committee, Coats declined to comment.
"I have always believed that given the nature of my position and the information which we share it's not appropriate for me to comment publicly on any of that," Coats said. "So on this topic, as well as other topics, I don't feel it's appropriate to characterize discussions and conversations with the president."
Coats said he was “not aware” of any attempts to contact other intelligence officials to drop the investigation into Flynn.
Though he would not confirm or deny The Post report, Coats said he would be forthcoming if he’s asked about it by special counsel Robert Mueller, who was appointed to investigate Russian interference in the 2016 election.
ABC News' Alexander Mallin contributed to this report.