WASHINGTON—Lawyers advising President Donald Trump in the Russia investigation hope to decide whether he should testify by May 17, the one-year anniversary of the appointment of special counsel Robert Mueller, Trump attorney Rudy Giuliani said Monday.

Mr. Trump’s legal team has long been divided on whether he should agree to a sit-down interview with Mr. Mueller, a decision that exposes him to legal perils but also could hasten the end of an investigation that has shadowed his presidency.

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