But what does the average American think? Recent polling has given us hints about whether a Warren pick would set Clinton up for success or failure.
The Massachusetts Senator -- known for her liberal policies and focus on economic inequality and Wall Street reform -- was one of the last prominent Democrats to endorse Clinton for President.
But a source familiar with the process, said Warren is on the VP short list and is currently being vetted as a potential running mate.
Here are five poll numbers that show why Clinton may (or may not) pick Warren as her number two:
1.More than half of leaned Democrats think Clinton should choose someone else for her VP
According to a recent CNN/ORC poll, over half of Democrats and Democrat-leaning independents believe that Clinton should select someone other than Warren as her vice president.
Fifty-four percent of respondents said that they would like to see someone other than Warren on the ticket, while only 34 percent of leaned Democrats said they would like to see the Massachusetts Senator as Clinton's pick. Given the importance of party unity in this election, these numbers do not work in Warren’s favor.
2. Liberals could be more likely to vote Clinton, but others may not
Polls show that picking Elizabeth Warren would help consolidate Clinton’s base -- but might not do much with independents and other key groups of voters.
Clinton has had trouble garnering the votes of independents and young voters during the primary process.
More than half of voters -- 51 percent -- say choosing Warren would have no impact on their vote and the rest are about evenly divided. Independents and undecided voters say the same thing, according to a national Monmouth University poll released last week.
But 48 percent of liberal and 38 percent of Democrats say a Warren pick would make them more likely to choose Clinton in November.
3. Warren is one of her most popular options among Democrats
In the same Monmouth poll, 38 percent of Democrats said that they would be more likely to vote for Clinton if Warren were her running mate. Only 11 percent of Democrats said such a choice would make them less likely to vote for the presumptive Democratic nominee.
Only Bernie Sanders fared better than Warren in a potential pairing, with 53 percent of Democrats saying they would be more likely to vote for Clinton if she selected Sanders as her running mate. Such a pairing is highly unlikely, however, leaving Warren as the next best choice.
Other options in the poll included Senators Tim Kaine, Cory Booker, and Al Franken, as well as Secretary of Housing and Urban Development Julian Castro. Each of these options left a negative impression, with respondents saying they would be less likely to vote for Clinton if she chose any of these men as her VP.
4. Picking two women won’t make much of a difference
If Clinton chose the Massachusetts senator as her vice president, Clinton would make history again – this time headlining a major party’s presidential ticket alongside another woman.
But just how much of a difference would that make? According to a CNN/ORC poll released on June 22, not much.
When asked how Clinton choosing a woman as her running mate would impact votes, a mere 4 percent said they would be more likely to vote for the pair, 10 percent would be less likely to vote for them, and a whopping 86 percent said it would not make a difference.
5. More than a quarter of registered voters have never heard of Elizabeth Warren
Elizabeth Warren is still an unfamiliar face to many people across the country. Four in 10 registered voters say they either haven’t heard of Warren or don’t know enough to have an opinion of her, according to a recent CNN/ORC poll.
That number spikes at 48 percent of people in the Midwest, where Clinton needs to hold states like Michigan and Wisconsin, while scooping up states like Iowa and Ohio.
Warren’s favorability rating is just barely above water, with 31 percent seeing her as favorable and 29 percent seeing her as unfavorable.