In revoking Brennan's clearance, Trump on Wednesday accused the former Central Intelligence Agency director, one of his most outspoken critics, of making "a series of unfounded and outrageous allegations - wild outbursts on the internet and television - about this Administration".
Burr says if the claim is based on intelligence Brennan received while CIA director, it should have been included in the 2017 US intelligence assessment of Russian meddling in the election.
Mr. Trump, speaking to reporters on the White House South Lawn, said the official, Bruce Ohr, is a "disgrace".
In an opinion piece in The New York Times, Brennan said Trump's decision, announced Wednesday, to deny him access to classified information was a desperate attempt to end Mueller's investigation.
Describing Trump's move as "inappropriate and deeply regrettable", they insisted "we have never before seen the approval or removal of security clearances used as a political tool, as was done in this case". Writing in The Washington Post, William H. McRaven said he would "consider it an honor" if Trump would revoke his clearance, as well.
Democrats accused the president of trying to punish his critics.
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McRaven denounced Trump's recent unprecedented decision to revoke the security clearance of former CIA Director John Brennan, a fierce critic of the president. He said the only question now is whether the collusion that took place "constituted criminally liable conspiracy".
According to emails reported last week, Steele, a former British spy, kept in close contact with Ohr even after the Federal Bureau of Investigation cut ties with him as a source, with Steele continuing to send along information.
President Donald Trump is linking his decision to revoke the security clearance of former CIA Director John Brennan to the special counsel's investigation into Russian Federation election meddling and possible ties to the Trump campaign.
He went on to say that Ohr's actions related to Steele and the dossier are "disqualifying" for Special Counsel Robert Mueller, who's investigating Russian election meddling and potential collusion with the Trump campaign.
Former officials often retain security clearance after leaving office to allow their successors to consult them on issues of the day.
"So I think it's something that had to be done", he added. He told the Journal he doesn't trust "many of those people on that list" and thinks they aren't "good people".