On November 10, 2016, two days after his stunning election victory, Donald Trump met with President Barack Obama, alone, in the Oval Office, for 90 minutes. They covered plenty of important ground, including the nuclear threat from North Korea and the need—at least in Obama’s view—for the United States to uphold its part in the Paris climate agreement and the Iran sanctions deal. They also talked about Michael Flynn.

That last item is the one that may interest special counsel Robert Mueller. As his investigation of Russian meddling in the 2016 campaign draws closer to the current occupant of the White House, Mueller will want to determine what Trump knew about Flynn’s entanglements, and when he knew it, and what Trump was told about Russian interference in the election. Which could lead to an apparently unprecedented circumstance: a former president being interviewed as part of an investigation into his immediate successor. “If you are doing an obstruction of justice investigation, you would want that information,” says Solomon Wisenberg, who questioned President Bill Clinton as part of independent counsel Kenneth Starr’s probe. “Why is Trump trying to protect Flynn, saying ‘he’s a good guy,’ after all these people—the former president, Sally Yates—warned him?”

Current and former Obama insiders don’t believe such a step will be necessary. “Once Trump became the Republican nominee, leaders of the intelligence community briefed him periodically, and after the election more regularly,” says Ned Price, who was a C.I.A. analyst before becoming a National Security Council staffer and a special assistant to Obama, then quitting in February 2017 and publicly airing his dismay at Trump’s policies. “The briefings are scripted, documents are prepared, so it should be easy for Mueller to say, ‘I want to see the president-elect’s briefing for X day,’ or ‘Show me everything that was briefed to the president-elect about Russia.’ The process is led by the director of National Intelligence, but it involves analysts from C.I.A., N.S.A., F.B.I. So there wasn’t a need for President Obama, in that meeting, to delve into the nitty-gritty of what the intelligence community assessed and how they assessed it.”

Even so, Obama did feel an urgency to raise the issue of Flynn with Trump. Flynn, a star lieutenant general in Iraq and Afghanistan, had served as the head of the Defense Department’s intelligence agency in the Obama administration for a turbulent two years before being forced out of the job. He eventually became a vehement backer of the Trump campaign: “Lock her up! Lock her up! . . . Damn right! Exactly right!” Flynn yelled to a chanting crowd at the Republican National Convention. He then blasted Obama as a “weak and spineless” leader who “coddles” terrorists.

Yet Obama’s problem with Flynn was purely professional, his aides say. “It was already public that Trump was looking at Flynn for national security adviser,” an Obama operative who was briefed on the meeting says. “President Obama felt that the position is so important that you really need a serious person in there, and he suggested to Trump that he needed someone of higher caliber. Obama did wave him off of Flynn as N.S.A. adviser. But it was less about any possible corruption and more about competence, credibility, and character. It wasn’t related to Russian interference in the election. But yes, as far as the guts of the meeting in the Oval, on that Thursday, it was just the two of them.”