Former CIA directors John Brennan and Michael Hayden, former Director of National Intelligence James Clapper and former FBI Director James Comey are among the names considered, White House press secretary Sarah Huckabee Sanders said on Monday.
All have been tough on Trump in TV appearances.
The leaders have served in both Democratic and Republican administrations, including Trump's.
Former intelligence officials typically keep their high-level security clearances after leaving their government jobs, sometimes providing informal advice to current officials. Rand Paul, R-Ky., had tweeted that he would recommend that Brennan's security clearance be revoked asking "Is John Brennan monetizing his security clearance?"
At least two of the officials - Comey and McCabe - do not now have clearances.
Sanders would not say when the President would make the decision; she said only that the White House would provide updates when it had them.
"This is what totalitarianism looks like", Sen. McCabe spokeswoman Melissa Schwartz said the former deputy Federal Bureau of Investigation director's clearance was deactivated when he was sacked by Attorney General Jeff Sessions in March.
A spokeswoman for McCabe, Melissa Schwartz, wrote on Twitter that his security clearance was deactivated when he was terminated, according to what they were told was Federal Bureau of Investigation policy. "You would think the White House would check with the Federal Bureau of Investigation before trying to throw shiny objects to the press corps".
President Trump is considering the revocation of security clearances now held by former Obama administration officials; setting the stage for a high-stakes legal showdown with top government staffers.
Reached by phone, former Central Intelligence Agency and NSA director Michael Hayden had no comment on the White House's statement.
He tweeted that Trump's press conference was "nothing short of treasonous". Not only were Trump's comments imbecilic, he is wholly in the pocket of Putin. Sanders made her comments in response to a question about the meeting.
Clapper, interviewed by CNN, described the move as a "very, very petty thing to do".
But Mary Beth Long, the first woman confirmed to serve as the Assistant Secretary of Defense - she served in that capacity from 2007 to 2009 under former President George W. Bush - tweeted earlier this week: "If they want to be journalists, fine; but you can not be one with access to intel".
Democrats blasted the move as retaliation for free speech.