Additionally, he has already visited FBI headquarters, where he met with the counterintelligence agents who have been working on the case since last July, according to two people familiar with the matter.
In one memo, Comey wrote that Trump asked him to end the FBI probe into former national security adviser Michael Flynn, according to a person familiar with the matter.
One source added that part of Mueller's investigation is expected to focus on obstruction of justice. In that case, Comey would be a witness and Mueller will likely interview him as part of the probe.
Potentially complicating that effort is Comey's acceptance to testify on Capitol Hill after Memorial Day. The source says Comey likely will be limited with what he will be able to say now that the Russia probe is in the hands of Mueller.
"There's no way in the world Mueller wants his witness testifying," the source said. "He wants to question him before anyone else does but before that he'll have to go through tons of documents."
That means there will likely be a lot of negotiating happening in the early stages of the investigation particularly when it comes to congressional inquiries on the same material.
The source says Mueller is likely going to want to talk to people involved in the House and Senate investigations to make sure that he has the lead on everything involved with this investigation.
On Monday, Democratic Sen. Mark Warner of Virginia, the vice chairman of the Senate intelligence panel, told CNN that he and the committee's chairman, North Carolina Republican Sen. Richard Burr, hoped to meet with Mueller to talk about what Comey can and cannot say in his testimony.
"Our hope is that the chairman and I will be able to sit down and again just kind of get the rules of the road for us going forward with Director Mueller," Warner said.
Also on Monday, Republican Rep. Jason Chaffetz of Utah, chair of the House oversight committee, tweeted that he would postpone a planned Wednesday hearing because Comey told him he wants to speak with Mueller before testifying publicly.