The meeting in Washington came a day after Clinton shared a closed-door lunch with President Barack Obama, who defeated her in a hard-fought 2008 primary before recruiting her to be the top US diplomat.
Clinton, who has yet to say whether she will seek the presidency again, is already widely viewed as a frontrunner for the Democratic nomination.
Biden, who ran unsuccessfully for the Democratic nomination in 1988 and 2008, has hinted at a possible 2016 run.
The menu included scrambled eggs with roasted tomatoes and avocado, turkey bacon, fresh fruit and multi-grain toast, the vice president's office said in a statement.
More From This Section
The office did not say what they discussed.
The US president is limited to two four-year terms, meaning Obama will leave office in January 2017.
Earlier this year Clinton fielded a flurry of media questions about her intentions by saying only that she wanted rest and relaxation after a gruelling run as secretary of state.
The jet-setting diplomat visited some 112 countries and travelled over 950,000 miles in four years.
Age could emerge as a factor in the next presidential election. Biden will be 73 when the vote is held and Clinton will be 69. Obama was just 47 when he was elected in 2008.