Gore made the comment as the strolled with Fox on the grounds of U.S. Naval Observatory, where Gore maintains his official residence.
Reporters also heard Gore calling for the creation of "a community of North American democracy" but there was no elaboration.
Fox is using his two-day U.S. visit to outline his vision for a freer flow of people and goods across the border.
After his meeting with Gore, Fox planned an Oval Office visit with President Clinton and a luncheon with Secretary of State Madeleine Albright. He will meet with Gov. George W. Bush in Dallas on Friday.
Fox's proposal for an eventual opening of borders with United States has been greeted with skepticism by U.S. business and labor groups, but Clinton said Wednesday he wants to hear more before making a judgment.
"The devil is always in the details here, so I want to talk to him about it and see what he has in mind," Clinton said.
In Canada on Wednesday, Fox spoke to Prime Minister Jean Chretien about his goal of an integrated North America modeled in some respects after the European Union.
Chretien said he doesn't think it is feasible.
"We cannot establish relations between Canada, the United States, and Mexico in the same type of situation as in Europe," he said, adding that Canada wanted to maintain its own currency and refused to consider a common currency like the euro.
Fox said his goal was to promote prosperity, no matter the mechanism.
"We are not proposing a common currency here," he said. "We don't think that would work. We're proposing to work together â€“ work on human development, economic development â€“ to narrow the differences."
Despite reservations about his border proposals, Fox has won admiring comments from many Americans for having defeated the party that has run Mexico for more than 70 years.
They include some of Mexico's fiercest critics, such as Senate Foreign Relations Committee chairman Jesse Helms, R-N.C., and Thomas Constantine, a former director of the Drug Enforcement Administration.
Constantine said Wednesday he is impressed with Fox's willingness to fight corruption and organized crime in Mexico.
"I tend to be optimistic that an individual can change the dynamics of a situation," he said.