The former mayor wrote in an opinion article for The San Fransisco Chronicle that the vice presidency is a “dead end” and “not the job she should go for”.
“Historically, the vice presidency has often ended up being a dead end. For every George HW Bush, who ascended from the job to the presidency, there’s an Al Gore, who never got there,” he wrote on Saturday.
Mr Brown recommended that Sen Harris should ask for the position of attorney general instead, saying that the position has “legitimate power”.
“From atop the Justice Department, the boss can make a real mark on everything from police reform to racial justice to prosecuting corporate misdeeds,” he wrote.
“And the attorney general gets to name every US attorney in the country. That’s power.”
Mr Brown, who served as mayor in San Francisco from 1996 to 2004, has previously appointed Sen Harris to positions on the state Unemployment Insurance Appeals Board and the California Medical Assistance Commission.
The politician has spoken publicly about his previous relationship with Sen Harris, noting that they briefly dated over 20 years ago early in her political career.
Sen Harris is said to be one of the leading contenders to be Mr Biden’s running mate in the final days before his decision, following the promise Mr Biden made in his campaign to make a woman his VP pick.
Mr Brown continued in his editorial to warn Sen Harris against accepting the position on the basis that the administration would face a tough term in the midst of a pandemic and an economic downturn.
“The next few years promise to be a very bumpy ride. Barack Obama and the Democrats saved the nation from economic collapse when he took office, and their reward was a blowout loss in the 2010 midterm elections,” he said.
He also implied that the senator should plan for a future presidential run and that “being attorney general would give Sen Harris enough distance from the White House to still be a viable candidate for the top slot in 2024 or 2028, no matter what the state of the nation.”