Whatever the outcome of the encounter on Friday — which will be on the sidelines of the Group of 20 summit meeting of world leaders in Hamburg, Germany, but is expected to overshadow it — the Kremlin is betting that Mr. Putin can stage-manage the event so that he comes out looking like the stronger party.
If nothing much emerges from the meeting, analysts said, the Kremlin can repeat the standard Russian line that Mr. Trump is weak, hamstrung by domestic politics.
But if Mr. Trump agrees to work with Mr. Putin despite a list of Russian transgressions beginning with the annexation of Crimea and ending with its interference in the 2016 presidential election, he will also look weak while Mr. Putin can claim that he reconstructed the relationship.
“It is a win-win situation for Putin,” said Andrei V. Kolesnikov, a political analyst at the Carnegie Moscow Center.