Mr Trump will speak to Vladimir Putin, who the US President has praised, on Saturday
Sean Spicer, the White House's spokesman, tweeted the President would call the leaders of Russia, Germany and France on Saturday.
The Kremlin earlier said Russian President Vladimir Putin and Trump would speak.
Separately, a source in Berlin said Chancellor Angela Merkel would talk with Trump, although the German Chancellor's spokeswoman declined to comment.
Getting the most out of the 1st full week – tomorrow @potus will speak by phone with leaders of France, Germany and Russia
Mr Spicer, tweeting from the official Press Secretary account, said: "Getting the most out of the 1st full week – tomorrow @potus will speak by phone with leaders of France, Germany and Russia."
French President Mr Hollande and Merkel held a joint news conference earlier on Friday.
Getting the most out of the 1st full week- tomorrow @potus will speak by phone with leaders of France, Germany and Russia
— Sean Spicer (@PressSec) January 27, 2017
Theresa May arrived in the States on Thursday and is due to speak with Mr Trump face-to-face later today as she becomes the first global leader to meet with the President since his inauguration last Friday.
They will then hold a joint press conference at 1pm local time (6pm GMT) before a working lunch with Mr Trump and the Vice-President, Mike Pence.
Mrs May leaves the country at 10.30pm GMT.
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The two leaders will spend about an hour in face-to-face talks in the Oval Office, where President Trump has restored a bust of Winston Churchill removed by predecessor Barack Obama.
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Prime Minister Theresa May speaks during the 2017
Yesterday, in a speech to Republicans in Philadelphia, Mrs May cited Cold War President Ronald Reagan as she said the United States should engage with Russia but warned it should "beware" of Mr Putin.
Mr Trump has previously spoken of his admiration for the Russian president, something which has caused great concern to other Western leaders.
Russia's embassy in the UK has accused the British Prime Minister of trying to revive Cold War animosities with her warning against Russia.
Mrs Merkel and Mr Hollande met in Berlin today
Diplomats at the Russian embassy in London responded on Twitter today in rhyme.
They tweeted: "'Engage but beware', Prime Minister said. As far as we're aware, Cold War was long dead."
In her high-profile foreign policy speech on the eve of her meeting with Mr Trump, Mrs May said: "When it comes to Russia, as so often it is wise to turn to the example of President Reagan who – during negotiations with his opposite number Mikhail Gorbachev – used to abide by the adage 'trust but verify'.
"With President Putin, my advice is to 'engage but beware'.
The Russian embassy in London tweeted out a rhyme in defence of Mr Putin
"There is nothing inevitable about conflict between Russia and the West. And nothing unavoidable about retreating to the days of the Cold War. But we should engage with Russia from a position of strength.
"And we should build the relationships, systems and processes that make cooperation more likely than conflict – and that, particularly after the illegal annexation of Crimea, give assurance to Russia's neighbouring states that their security is not in question.
"We should not jeopardise the freedoms that President Reagan and Mrs Thatcher brought to Eastern Europe by accepting President Putin's claim that it is now in his sphere of influence."
Mrs Merkel's advisers are believed to have given up on any hopes Mr Trump will behave in a statesmanlike manner.
They have reported being unable to effectively communicate with Mr Trump's advisers and believe he may not honour existing trade agreements involving their country's agreement.
Talking about Mr Trump behaving like a president, one German adviser, said: "None of us here believe that anymore.
"The Americans, and the world, will get the Trump they elected."
Vice Chancellor Sigmar Gabriel today said: "We have to prepare for a rough ride."