For President Trump, anytime is a good time for deal-making, but never more so than now with the leaders of China and Russia.

Last week, Mr. Trump said he wanted to normalize commerce with Russia, appearing to lessen the pressure on Moscow to settle its war with Ukraine. And he is trying to limit the fallout from his own global trade war by urging China’s leader to call him.

“We all want to make deals,” Mr. Trump said in a recent interview with Time magazine. “But I am this giant store. It’s a giant, beautiful store, and everybody wants to go shopping there.”

Mr. Trump may have something even bigger in mind involving Russia and China, and it would be the ultimate deal.

His actions and statements suggest he might be envisioning a world in which each of the three so-called great powers — the United States, China and Russia — dominates its part of the globe, some foreign policy analysts say.

It would be a throwback to a 19th-century style of imperial rule.

Mr. Trump has said he wants to take Greenland from Denmark, annex Canada and re-establish American control of the Panama Canal. Those bids to extend U.S. dominance in the Western Hemisphere are the clearest signs yet of his desire to create a sphere of influence in the nation’s backyard.

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