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The prime minister is also expected to get updates from Washington on the international response to the virus after leaders of the G7 nations met last week.
Johnson, who is still recovering from the disease at Chequers after a stint in intensive care, is also expected to have an audience with the Queen later this week.
His official spokesman stressed he is not yet well enough to work, however, and will not be at the despatch box in parliament for PMQs tomorrow.
The PM’s official spokesman said on Tuesday that Johnson and Trump would speak at 2pm.
“Part of the call will be for the PM to thank the president for messages of support he has sent to him,” the spokesman said.
“It is also the case that it will allow the PM to get an update on the international response to coronavirus.”
The two leaders will speak after Trump chose to suspend all immigration to the US “in light of the attack from the invisible enemy” and as allegations swirl about China’s handling of the outbreak.
The US is currently chair of the G7 group of nations, who last week discussed pressing for an inquiry into Beijing’s response to the contagion, which began in the Hubei province city of Wuhan.
The phone call with the Queen will be the first time the monarch and PM have spoken for some three weeks.
Johnson’s spokesman added that the PM has spoken to Dominic Raab who is deputising as first secretary of state, and senior advisers such as Dominic Cummings in recent days.
Johnson also yesterday sent a message of condolence to Justin Trudeau after the shootings in Canada.
The spokesman added: “The PM is continuing his recovery at Chequers and is not formally doing government work. He has been receiving updates Number 10 on the coronavirus response and has spoken with the first secretary of state and senior members of his team.”
Raab took part in the G7 conference call on behalf of the PM last week.
At the Downing Street press conference following the call, he said a “deep dive” review of China’s response to the disease should be carried out.
In a marked change in tone with Beijing, he said it would not be “business as usual” after the pandemic and there was “no doubt” China would face a probe.
“I think there absolutely needs to be a very, very deep dive after the event review of the lessons - including of the outbreak of the virus - and I don’t think we can flinch from that at all, it needs to be driven by the science,” he said.
Raab, who is also the foreign secretary, will take questions from new Labour leader Keir Starmer at PMQs on Wednesday as part of the new virtual parliament. Raab is expected to be in the Chamber while Starmer will ask questions via Zoom from his office.