"I'm ready to help in any way I can because I think this will be a moment where every American – I don't care what party you are, I don't care what age, race, gender, I don't care – every American should want to fix our country," Ms Clinton said.
"So if you're asked to serve, you should certainly consider that," she added during a virtual appearance at the 19th Represents Summit.
Ms Clinton would face an uphill battle getting confirmed in a GOP-run Senate. Republicans slammed her during her tenure as the country's top diplomat and after. Her handling of an attack at a US diplomatic facility in Benghazi, Libya, and others matters drew constant scrutiny from Republicans.
Ms Clinton had some advice for the media as she hailed California Democratic Senator Kamala Harris joining Mr Biden on the Democratic presidential ticket.
"I still hope, especially with Kamala on the ticket, that the coverage of women running for president or vice president will be less sexist, less sensationalist and less trivializing," Ms Clinton said.
If they can defeat the president and Vice President Mike Pence, she said the duo would be "inheriting a mess of historic proportions."
"I think Joe and Kamala together will be absolutely ready for lots of long, long days and very short nights working to get as much done as quickly as possible," she said.
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