Mueller is seeking to interview Director of National Intelligence Dan Coats and National Security Agency Director Mike Rogers, according to the people, who asked for anonymity because of the sensitivity of the matter.
Former United States attorney Barbara McQuade, who served under the Barack Obama administration, told the Daily Beast if Trump fired Mueller "and it could be shown that his goal was to impede the investigation, it could be additional evidence of obstruction of justice".
The Washington Post story prompted a furious reaction from Mr Trump's personal lawyer, Marc Kasowitz, who issued a statement saying the Federal Bureau of Investigation was behind the story.
The investigation into ties between President Trump's campaign and the Russian government has now turned to investigating Trump himself for obstruction of justice, the Washington Post reported Wednesday.
Mark Warner of Virginia, the panel's top Democrat, didn't provide any details on the meeting, and said in a statement they "look forward to future engagements" with Mueller.
President Trump visits Scalise, other shooting victims at hospital
Brooks said even after one of the officers was wounded, he limped toward the outfield in an attempt to help Scalise. As far as that game they were practicing for, it's set to go on as planned on Thursday.
Comey told senators on June 8 that Trump's shifting explanations for dismissing him were "lies, plain and simple".
It's not true anymore, according to a new report by the Washington Post.
At last week's hearing, Comey suggested that he believed Trump was plausibly guilty of obstruction of justice.
Many expected that Mueller would at some point turn to the topic of whether the president obstructed justice.
A spokesman for the DNI declined to comment to CNN.
There were claims earlier this week that Mr Trump was also considering "terminating" Mr Mueller.
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