The president's lawyers have cautioned him not to take wide-ranging questions from Mueller's team for its Russia investigation, The New York Times reported , citing four sources briefed on the matter. Trump has a history of making false claims, and lawyers worry he could get charged with lying to investigators, according to the newspaper.

President Donald Trump may not voluntarily take questions from special counsel Robert Mueller, after all.

The president has publicly said he wants to speak with Mueller about the probe into Russian efforts to influence the 2016 election. That investigation includes looking into whether the Trump campaign coordinated with the Kremlin and, reportedly, whether he obstructed justice.

A refusal to take questions could lead Mueller to compel Trump to testify before a grand jury, the Times reported. That scenario could spark a legal battle ahead of this year's midterm elections in November.

Asked for comment, one of Trump's lawyers, Ty Cobb — whom the Times describes as one of the few advisors urging Trump to cooperate — said discussions are ongoing between the office of the special counsel and the president's legal team, but he didn't shed more light on the situation beyond that.

"The professional and active discussions between the OSC and the President's personal lawyers regarding how and under what terms information will be exchanged are understandably private," Cobb told CNBC in an emailed statement.

Read the full Times story here.