He has already been subpoenaed by the House Permanent Select Intelligence Committee.
Mr Mueller was appointed as special counsel to investigate Moscow's involvement in the presidential election past year and possible collusion by Trump campaign associates with the Russians, but there has been no indication that Mr Mueller told the president to fire Mr Comey.
"The message the president is sending through his tweets is that he believes the rule of law doesn't apply to him and that anyone who thinks otherwise will be fired".
Feinstein also is a member of the Senate Intelligence committee, which is conducting its own Russian Federation probe.
The obstruction of justice investigation into Trump began days after Comey was sacked, people familiar with the matter told the Washington Post.
Deputy Attorney General Rod Rosenstein, to whom the special counsel investigating Russia's meddling in the 2016 presidential election now reports, has privately discussed the possibility that he may need to recuse himself from the matter, according to ABC News.
Special counsel Mueller - a respected former Federal Bureau of Investigation director - was also bringing in legal firepower to investigate whether there was collusion between Trump's team and Russian Federation to fix the 2016 election or an attempted cover-up.
After meeting with Mueller in a classified session, the leaders of the Senate panel indicated that their inquiry would steer clear of obstruction of justice to focus instead on Russian Federation meddling in the elections - and whether there was any Trump campaign collusion with officials tied to the Kremlin.
In a report published on Wednesday, the paper quoted five people briefed on the requests, saying those who agreed to be interviewed include national intelligence director Daniel Coats, Admiral Mike Rogers who heads the National Security Agency (NSA), and his recently departed deputy, Richard Ledgett.
Also unclear was whether the president's comment confirming he was under investigation was based on direct knowledge or media reports that Mueller is examining whether the president obstructed justice by firing Comey last month. Trump said on Twitter, appearing to refer to Deputy Attorney General Rod Rosenstein.
Except: Anyone who's anyone in Washington has discouraged him from this - or from firing Mueller, period.
"This is the single greatest witch hunt of a politician in American history!" the United States president tweeted. "Regulations way down, jobs and enthusiasm way up!" said the US President in another tweet.
The Labor Department this month that the jobless rate fell to 4.3 percent the lowest level since 2001, from 4.4 percent. Although Trump is a known mercenary who won't hesitate to stab allies in the back when it suits him, he won't let go of his loyalty to Flynn.
Trump has denied any involvement with the Russians during the campaign and has called media reports of collusion a "hoax" and a "phony story".
"In fact when I made a decision to just do it", the president acknowledged, "I said to myself, I said 'you know, this Russian Federation thing with Trump and Russian Federation is a made-up story, it's an excuse by the Democrats for having lost an election that they should have won'".