"Even if it's only to a slight degree, the president will step back and claim victory," said Cashin, director of floor operations for UBS at the New York Stock Exchange.
Trump is threatening tariffs on European auto imports. In an interview with "Squawk Box" last week, Commerce Secretary Wilbur Ross said it's too "premature" to say whether Trump's auto tariffs will come to pass but did not rule them out.
International trade tensions, including Friday's first salvo in America's trade war with China, continue to dominate headlines as Trump gets ready to leave Tuesday on a swing through Europe. The president's trip includes meetings in Brussels with NATO allies, London with British Prime Minister Theresa May, and Helsinki with Russian President Vladimir Putin.
But Cashin said Trump's trade fights are "temporarily" investors' friends, adding the market expects it could keep the Federal Reserve on hold.
The Fed hiked its benchmark short-term interest rate a quarter percentage point in March and June, and indicated two more increases were likely this year.
The trade tactics have "kind of been I'll match you and you'll match me," Cashin said in a "Squawk on the Street" interview. "The Fed will watch them, but they won't be ready to rush in for fear what's going on."