Trump has long prized his instincts for taking advantage of an adversary's weaknesses, and referred to the "turmoil" confronting May at home in remarks to reporters.
The Prime Minister faces a rebellion from advocates of a hard break from the European Union, who say she has been waffling, and is in danger of losing control. Johnson, a potential successor to May, resigned yesterday as Foreign Secretary.
Trump praised him in personal terms: "Boris Johnson is a friend of mine. He's been very, very nice to me and very supportive. And maybe we'll speak to him when I get over there. I like Boris Johnson. I've always liked him."
Trump's seven-day journey begins in Brussels and will take him to England for his first visit there as president, to Scotland for a weekend respite at his private golf course and finally to Helsinki for his tête-à-tête with Putin.
European leaders are as concerned about what concessions he might make to Putin - such as recognising Russia's annexation of Crimea from Ukraine - as they are about the chaos he could create at the Nato summit.
May plans to roll out the red carpet for Trump and first lady Melania Trump at a gala supper on Friday at Blenheim Palace and at a luncheon on Saturday at Chequers, the prime minister's country estate. She also secured him an audience with the Queen at Windsor Castle.
It was a startling gambit for Trump to risk offending his host by showering Johnson with praise while May faces threats of a revolt - even a no-confidence vote - by her own Conservative Party over how she is handling Brexit.
"Trump goes after the weak people. He smells who is weak and who is strong, and he gets on well with the strong ones," said Robin Niblett, director of the Chatham House, a prominent think-tank in London.
To her critics, May is forever making compromises to carry out Brexit, even though she herself voted against leaving the European bloc. She has not helped her image by endlessly kicking the can down the road and delaying decisions.
Alternatively, Johnson could be seen as strong by Trump because he pushed for Brexit, he won - and when he didn't get what he wanted, he quit. In a leaked audiotape, Johnson also praised Trump as the consummate dealmaker.
"Imagine Trump doing Brexit. He'd go in bloody hard," Johnson said. "There'd be all sorts of breakdowns, all sorts of chaos. Everyone would think he'd gone mad. But actually you might get somewhere."
Trump seizing on perceptions of weakness in the diplomatic arena is in keeping with how he dealt with rival developers and other adversaries in real estate deals, according to Trump biographer Michael D'Antonio.
"There are certain fail-safe bully tactics that can be employed when you're the stronger, bigger kid," D'Antonio said. "He is willing to be extreme and seek the upper hand, especially with people that he perceives to be polite and well-mannered."
That impulse may be strongest this week with Merkel, who has been a stalwart against Trump's disruptions in Europe but whose standing took a blow last month when she confronted the most serious leadership challenge in her 13-year rule of Germany.
Trump loathes Germany's trade imbalance with the US and feels the country is free-riding off the US security umbrella. He also has long criticised Merkel for her 2015 decision to admit more than one million asylum seekers from Syria and elsewhere, warning that they were a proverbial Trojan horse who could destroy Europe's way of life.
Trump has tried to spotlight any signs of Merkel's political troubles, tweeting last month that "the people of Germany are turning against their leadership as migration is rocking the already tenuous Berlin coalition."
In Brussels, Merkel will defend her decision to raise defence spending more slowly than Trump's goal and seek to maintain the 35,000 US troops deployed to Germany, which Trump has threatened to pull back.
But Merkel has actually benefited at home from Trump's attacks, since the US President is deeply unpopular among the German electorate, as he is with voters across much of western Europe.
Other sometimes-adversaries of Trump will be in Brussels as well, including French President Emmanuel Macron and Canadian Prime Minister Justin Trudeau, creating the potential to extend disagreements that upended last month's Group of Seven leaders summit in Quebec. Trump left that gathering without signing the perfunctory joint statement among the leaders that his aides had endorsed, and he proceeded to trash its host, Trudeau, as "weak" and "dishonest."
Ahead of the Nato meetings that begin tonight NZT, Nato Secretary-General Jens Stoltenberg tried to strike an optimistic note and play down the simmering disputes.
"Our summit comes at a time when some are questioning the strength of the transatlantic bond and I would not be surprised if we have robust discussions at the summit, including on defense spending," Stoltenberg told reporters. "Different views are normal among friends and allies, but I am confident that we will agree on the fundamentals."
But European Council President Donald Tusk was more direct in anticipating that Trump may have designs on sowing discord, delivering a stinging warning to the visiting American president.
"Dear America, appreciate your allies," Tusk said. "After all, you don't have that many."
As he departed the White House, Trump offered a rebuttal.
"Well, we do have a lot of allies," he told reporters before boarding Marine One.
"But we cannot be taken advantage of. We're being taken advantage of by the European Union. We lost US$151 billion last year on trade. And on top of that, we spend at least 70 per cent for Nato. And, frankly, it helps them a lot more than it helps us. So we'll see what happens. We have a long, beautiful week."
