"I think Bernie needs space to decide what he wants to do next, and he should be given the space to do that," she told the hosts. "Right now, I'm focused on what we're going to do next in this crisis around the coronavirus."
But after the South Carolina primary last month breathed new life into Biden's campaign, he's become a clear Democratic front-runner.
Warren praised Biden on the show, applauding his promise to partner with a woman as vice president on his ticket.
"I really was heartened to see the vice president say it’s time to have a woman at least somewhat close to the White House,” she said. "He understands we are a changing electorate, and we are changing what we see as leadership… I was glad to see it.”
However, she said, so far "no one has asked” if she would accept the job.
As the coronavirus crisis continues to sweep across America, Warren called for measures to ensure the Democratic process isn’t affected.
"Democracy is based on the notion that people vote. So what we should be doing … is doing vote by mail," she said. "Let's get that up and organized. Let's find ways for people safely to be able to vote remotely."
She added, "We need to be putting this in place as quickly as we can for the primaries, but also we need this in place by the time we hit our fall elections."
Dozens of people were infected with the COVID-19 virus during a Biogen conference in Boston.
Asked by the hosts on whether she'd support shelter-in-place policies -- where people are encouraged to stay indoors, likely their homes, until told otherwise -- in her home state of Massachusetts, Warren didn't say yes or no.
Instead, she pushed that health officials and scientists are "speculating" how bad this virus really is -- as without proper testing, they don't truly know how many people have the virus.
"Let me start by saying … we don't have enough testing kits. That's true in many places around the country," she said. "So whether we have 250 cases that are confirmed here or 2,500 cases, or even more than that … the doctors and scientists are speculating."
She added, "Without enough tests, how do you know?"
Warren told the hosts that the issue shouldn't be a political decision, but Americans should listen to the doctors more closely.
"This should be a decision that the epidemiologists and others make," she said. "I will follow their orders."