There will be no adoring throngs that would greet a new running mate in a routine campaign.
In private, former president Barack Obama suggested to others that he believed Harris was the favorite.
Democrats close to the campaign say an announcement is imminent, and could come as early as Tuesday.
The leading contenders include California Sen. Kamala Harris, California Rep. Karen Bass and Obama national security adviser Susan Rice.
The California representative and former state Assembly speaker has emerged as a leading challenger to be Joe Biden's running mate.
"It'd be a good move for Republicans," Sen. Lindsey Graham (R-S.C.) said when asked about President Obama's former national security adviser.
The presumptive Democratic presidential nominee has vowed to select a woman as his nominee for vice president.
As few as six serious contenders are entering a second round of vetting to become a potential vice presidential nominee.
The former vice president declared he will pick a female running mate and has floated several potential choices.
Asked if she would accept a position as Biden’s running mate, Warren gave a one-word answer: “Yes.”