President Donald Trump’s lawyers are considering ways for him to testify before special counsel Robert Mueller, provided the questions he faces are limited in scope and don’t test his recollections in ways they say could unfairly trap him into perjuring himself, a person familiar with his legal team’s thinking said.

Mr. Trump’s legal team is weighing options that include providing written answers to Mr. Mueller’s questions and having the president give limited face-to-face testimony, another person familiar with the matter said. “Everything is on the table,” this person said.

Mr. Mueller is investigating whether Mr. Trump’s campaign colluded with Russia in the 2016 elections and whether the president obstructed justice when he fired former Federal Bureau of Investigation Director James Comey, who launched the Russia probe.

The president denies his campaign colluded with Moscow and that he obstructed justice; Russia says it didn’t meddle in the campaign.

Mr. Mueller this month secured an indictment against three Russian companies and 13 Russian citizens for allegedly engaging in a widespread effort to interfere in the 2016 presidential election, including inventing fake personas on social media and staging rallies with the “strategic goal to sow discord in the U.S. political system.” The indictment didn’t accuse the Trump campaign of assisting that effort.