Vice President Joe Biden, if he had entered the 2016 White House race, would have chosen progressive stalwart Elizabeth Warren as his running mate, according to a new report by Politico.

Biden discussed the possibility with Warren, a Massachusetts senator, during a meeting at his Washington, D.C. residence in August, when Biden was still pondering the launch of a presidential bid. Biden put his 2016 ambitions to rest, however, in October, citing concerns for his family after the death of his son Beau earlier in the year.

Politico reports that Biden had told Warren during the conversation that he wanted her to be his vice presidential pick, but he did not ask her outright to commit to the position or endorse him.

Warren, according to Politico, appeared "non-committal" but "not displeased" with the meeting.

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Biden still believes that Warren, a harsh critic of big banks and one of the Senate's strongest advocates for Wall Street reform, is the ideal candidate for the vice presidential slot.

Biden recently "told associates that Warren would be an equally smart pick for Hillary Clinton," reports Politico.

A Clinton-Warren ticket could potentially patch the cracks in the Democratic party brought about by a vicious primary cycle. Warren's anti-Wall Street bona fides could bring more credibility to Clinton, who has struggled with support from the party's more leftist, activist base because of her own ties to the financial sector.

As for the Massachusetts senator's thoughts on the No. 2 slot, Warren has not ruled out the possibility of running alongside Clinton, should she be asked.

"We've got to get all of our nominations settled on the Democratic side," Warren told Mic earlier this week. "For me, I'm going to keep doing my job every single day and I'm not thinking about another job."