"He's very interested and thought it was very good to have the meeting,” Gibbs said. “But in a phrase you'll hear in exceedingly large numbers of times between now and the 20th of January, there's only one president at a time."
Other members of Obama's transition team might meet with the foreign leaders, Gibbs said.
After touring the White House and meeting with President Bush on Monday, Obama headed back to Chicago, where he is expected to remain for the rest of the week with Vice President-elect Joe Biden to work on the transition.
Gibbs said he believes Biden is back in Chicago after being spotted Sunday at the Philadelphia Eagles game, an appearance that surprised Obama aides.
"My wife said, ‘What's he doing there?' " Gibbs recounted jovially. And I said, 'That's a darnn good question.' "
Obama does not plan to announce any Cabinet selections this week, although he might make White House staff appointments. He made three phone calls while sitting on the tarmac Monday in Washington, one of which was to Sen. Richard G. Lugar (R-Ind.), who has been speculated as a possible cabinet nominee, possibly as secretary of State.
Obama is likely to lay a wreath Tuesday in observance of Veterans Day. He may do some shorter trips over the next few weeks and is expected to travel to Hawaii around Christmas time, Gibbs said.