Several of Joe Biden's allies say they could see the former vice president picking Sen. Elizabeth Warren (D-Mass.) as his running mate to help unify the centrist and progressive wings of the party.

The speculation comes after Biden pledged to pick a woman as his running mate during the Democratic primary debate on Sunday.

Picking Warren would have its drawbacks, however, putting two septuagenarians at the top of the ticket from safe blue states.

"I think she represents a sort of bridge between the moderate land and progressive lane," said one longtime Biden ally who is in touch with the campaign.

"I'm hoping he goes with Kamala," the ally added, referring to Sen. Kamala Harris (D-Calif.), who is one of several women mentioned as potential running mates. "I just don't think he'll do it."

Another Biden ally, who has also spoken to the campaign regularly, said Warren "makes the most sense."

"There are a lot of qualified women, but she would be the best choice without a doubt," the ally said.

Warren herself before ending her presidential campaign sought to present herself as a unity candidate who could help the Democratic Party's fractious branches come together against President Trump.

"The way I'm going to win is I'm going to unite our party because we have to have a united party," Warren said at a town hall in New Hampshire last month. "We can't have a repeat of 2016."

"She would definitely help shore up some of his support on the left flank and with women, and especially in the coronavirus crisis, [it] definitely helps show a ticket that is qualified, has plans to deal with it," said Democratic strategist Eddie Vale.

Vale and other Democrats said it would be foolish for Warren to not be on a shortlist for Biden, particularly as Biden has largely embraced her position on bankruptcy in recent days.

Warren hasn't yet endorsed a candidate in the race, though both Biden and his chief rival for the nomination, Sen. Bernie Sanders (I-Vt.), are angling for her support.

Over the weekend, Biden endorsed Warren's bankruptcy plan, saying that "few people in the country understand how bankruptcy hurts working families more" than the Massachusetts senator. And in the Democratic debate Sunday, he also acknowledged having a conversation with Warren about the plan over the weekend.

At the same time, Biden has indicated that he wants to pick a running mate with a similar vision for the country as his. That may make Warren a difficult pick.

"For me, I think the most important thing in choosing the vice president is whether or not the person is simpatico with me in terms of where I want to take the country," Biden told MSNBC's Lawrence O'Donnell in an interview last week.

"We can disagree on tactic but not on strategy," he added. "And so that's the first test. And there are a number of women and African Americans as well who would meet that criteria for me."

Biden himself has pointed to a few possible contenders for vice president. At a town hall in Iowa in November, when asked whom he would choose as his running mate if he wins the Democratic nomination, he rattled through a list of potential picks, including former acting Attorney General Sally Yates and Stacey Abrams, the 2018 Democratic nominee for Georgia governor.

Other names that have been floated as potential running mates include Rep. Val Demings (D-Fla.) and Michigan Gov. Gretchen Whitmer.

Some Democrats said that Biden shouldn't just aim to choose a woman as his running mate but rather a woman of color. Doing so, they argue, would be a nod to the role that African American voters have played in resurrecting the former vice president's campaign in recent weeks.

"I think Joe Biden has to pick a person of color for his VP slot," Michael Starr Hopkins, a Democratic strategist, said. "If you look at what happened in South Carolina and the fact that the African American community saved his candidacy, I don't think it would just be a bad political move to not pick an African American candidate, but it would be a slap in the face."

Starr Hopkins said that the former vice president would be wise to take a serious look at Demings as his eventual running mate.

Demings, a second-term congresswoman and one of the House managers in President Trump's impeachment trial, has been floated as a potential running mate for the eventual Democratic nominee for months. Her clout in central Florida, a crucial battleground in the state, could help Democrats in their bid to recapture the state in November.

"There needs to be more focus on the map itself when we talk about these VP candidates. It's going to be a close race," Starr Hopkins said. "Democrats need to be thinking about not just these national numbers but how the running mate is going to contribute to the electoral vote."

While Biden's pledge to choose a woman as his running mate may be an acknowledgement of the current mood of the Democratic Party, it's unclear how or whether his eventual choice will play in the general election.

Christopher Devine, an assistant professor of political science at the University of Dayton in Ohio, said there's little if any evidence that picking a female running mate has an effect on overall electoral outcomes, noting that in 1984 and 2008, when women were on the ballot as vice presidential candidates, female voters were no more likely to cast their ballots for the Democratic or Republican tickets.

Devine - who's co-authoring a forthcoming book titled "Do Running Mates Matter?" - said Biden's decision to choose a woman as his running mate is more significant because of what it communicates to voters.

"What this does for Joe Biden is it helps shape how voters are thinking about him," Devine said. "And by pledging to pick a woman running mate, he's saying that he gets it, that he values the contributions of women in his White House and in the policies he carries out."