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.

In an interview, Mr. Giuliani said, “every day we swing a little different” on whether to advise Mr. Trump to talk to Mr. Mueller, though he suggested that recent developments in the probe have made him more leery.

The president’s initial position was “what do I have to lose? I’m telling the truth,” Mr. Giuliani said. But Mr. Trump has also promised to weigh his lawyers’ advice.