WASHINGTON (CNN) -- Sen. Barack Obama is beginning his search for a running mate, but Sen. John McCain's campaign denies speculation that he's interviewing vice presidential candidates at his home this weekend.
Sen. Barack Obama has quietly begun searching for a vice presidential candidate, a source says.
A veteran Democratic activist said former Fannie Mae CEO Jim Johnson has accepted Obama's request to begin a screening and selection process for the No. 2 spot.
Johnson performed a similar role for Democratic presidential nominees Walter Mondale in 1984 and John Kerry in 2004.
Meanwhile, McCain, the presumptive Republican nominee, is hosting top party figures at his home in Arizona this weekend, fueling speculation that he is starting his own search for a running mate.
But campaign advisers downplayed the visits, saying the gathering is not a vetting of potential running mates but only the McCains showing their gratitude to the 18 to 20 guests for their support.
Obama campaign spokesman Bill Burton declined to comment on the report of his candidate's running mate search.
The source, a party operative who has been involved in Democratic presidential campaigns and conventions for more than 20 years, said that the process is "at a very early point" but that campaign workers "have been informally thinking about it for a while."
In addition, former Deputy Attorney General Eric Holder will be part of Obama's vice presidential vetting team, a source close to the campaign said.
Holder held the No. 2 position in the Justice Department during the Clinton administration and was acting attorney general in the early days of the Bush administration.
Obama said Thursday that he is not discussing his selection process and does not have criteria for a running mate.
"No criteria right now. I still have to win the nomination," he said.
Although Obama is the Democratic front-runner and has captured a majority of pledged delegates after Tuesday's Kentucky and Oregon primaries, he has not clinched the 2,025 delegates needed to win the nomination against Sen. Hillary Clinton.
Despite the math, Clinton has vowed to remain in the race.
A longtime Democratic strategist familiar with other vice presidential searches called Johnson "a natural" for the role and said that choosing him was "very efficient because he has already vetted some of the people, like [former North Carolina Sen. John] Edwards and [New Mexico Gov. Bill] Richardson."
The "threshold question," the strategist said, was "whether Hillary Clinton is a part of the process or whether there's a conversation up front" that clarifies things.
House Speaker Nancy Pelosi, a California Democrat, was surprised Thursday to hear that Obama has started a search.
"I did not know that Sen. Obama had started his search for vice president ... but again, when it comes to vice presidents, I am not giving any advice unless asked about it by the candidates," she said.
"I think, though, that Hillary Clinton and Sen. Obama, both having a good chance to win the nomination, probably started thinking about who his or her running mate might be, what transition teams they might have, whether they should be briefed by the White House ... on issues of concern to our country," Pelosi said. Watch what Pelosi has to say about the vice presidential search »
Among the guests expected at McCain's ranch in Sedona, Arizona, are Florida Gov. Charlie Crist, Louisiana Gov. Bobby Jindal and former Massachusetts Gov. Mitt Romney, one of McCain's former rivals for the GOP presidential nomination.
Former Arkansas Gov. Mike Huckabee, another formal rival, was invited but cannot attend, a source said.
Other guests, according to an adviser, include Kansas senator and former Republican presidential candidate Sam Brownback, former eBay CEO Meg Whitman, FedEx founder Fred Smith and senior adviser Charlie Black.
But Black said, "He is definitely not interviewing anyone, and this weekend is not about that [vice presidential] process."
Obama and McCain face similar challenges in seeking a running mate, insiders say.
One of their top considerations must be age -- in Obama's case because of his relative youth, 46, and because McCain, at 71, is relatively old, according to a veteran Democrat who asked not to be named.
And both "need to focus strongly on national security," the source said.
McCain must select someone qualified to handle national security questions, or else it would indicate that he is choosing someone who is not qualified to be president. Watch a report on McCain's vice presidential options »
Obama's lack of a long record at the national level -- he has been a senator since 2005 -- leaves him with comparatively little national security experience.
That may make it less likely that Obama would choose a governor as his running mate, since they tend to have few national security qualifications, according to the source.
One exception might be Richardson, who has been involved in international diplomacy and was U.S. ambassador to the United Nations in President Clinton's administration.
CNN's John King, Gloria Borger, Jessica Yellin, Ed Hornick and Paul Courson contributed to this report.