It would be Mr Johnson’s first prime ministerial visit to the White House.
The meeting has reportedly been penned in for early next week.
Prime Minister Boris Johnson – In pictures
They will discuss Covid-19, China and climate change – according to Axios.
On Thursday, No 10 said it could not confirm whether Mr Johnson will meet US president at the White House next week when he will be stateside for the United Nations general assembly.
His official spokesman said: “I’ve seen some speculation on that but there are no confirmed plans.”
On Wednesday, Mr Johnson teamed up with US President Joe Biden and Australian Prime Minister Scott Morrison to confirm the creation of a “new trilateral defence partnership”.
Mr Johnson said: “I’m delighted to join President Biden and Prime Minister Morrison to announce that the United Kingdom, Australia and the United States are creating a new trilateral defence partnership, known as Aukus, with the aim of working hand-in-glove to preserve security and stability in the Indo-Pacific.
“We are opening a new chapter in our friendship.
“Perhaps most significantly, the UK, Australia and the US will be joined even more closely together, reflecting the measure of trust between us, the depth of our friendship, and the enduring strength of our shared values of freedom and democracy.
“Now the UK will embark on this project alongside our allies, making the world safer and generating jobs across the United Kingdom.”
