Trump has history of lying in court so I would be amazed if he didn't lie to Mueller as well - he is utterly incapable of keeping to the truth (even under oath) and his minions know that.
Some of the WaPo article:
Behind the scenes, Trump has told his team of lawyers that he is not worried about being interviewed, because he has done nothing wrong, according to people familiar with his views. His attorneys also support a sit-down, as long as there are clear parameters and topics.
However, some of Trump’s close advisers and friends fear a face-to-face interview with Mueller could put the president in legal jeopardy. A central worry, they say, is Trump’s lack of precision in his speech and his penchant for hyperbole.
People close to Trump have tried to warn him for months that Mueller is a “killer,” in the words of one associate, noting that the special counsel has shown interest in the president’s actions.
Roger Stone, a longtime informal adviser to Trump, said he should try to avoid an interview at all costs, saying agreeing to such a session would be a “suicide mission.”
“I find it to be a death wish. Why would you walk into a perjury trap?” Stone said. “The president would be very poorly advised to give Mueller an interview.”