Biden acknowledged the mayor, a former NBA player, during the event in Washington, D.C.
"And I told the president, next game, I have him," said Biden. "Just remember, I may be a white boy, but I can jump."
The quip, referencing the 1990s film starring Wesley Snipes and Woody Harrelson, was followed by laughter.
"I think we can take him," Biden said.
This is the second reference to California this week for the vice president. During an appearance on "Late Night With Seth Meyers," Biden praised Gov. Jerry Brown's involvement with the high-speed rail project.
Jerry Brown is leading the country in having high-speed rail," Biden said. "I mean by high-speed rail, rail that can go 230, 240 miles an hour. It’s environmentally more sound, it is economically more sound, it makes sense in every way and it’s about time we get up and do it.