Former Vice President Joe Biden this week dismissed the idea of New York Gov. Andrew Cuomo as his running mate, doubling down on his previous vow to have a woman on the ticket.

During the coronavirus outbreak, Cuomo has been seen by many as a political star among Democrats for his handling of the crisis in his state. Some have even floated the idea that he should be Biden's vice presidential pick.

Appearing on CNN's coronavirus town hall on Thursday, a virtual attendee brought the possibility of a Biden-Cuomo ticket to the former vice president and presumptive nominee's attention.

"Despite your previous pledge to pick a woman for vice president, would you reconsider that for a qualified candidate who has performed admirably during this crisis, like Governor Cuomo? " small business owner Evan Eads asked.

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"I think that Governor Cuomo is capable of being president. I think he's a great guy, but I also think that it's important that there be a woman," Biden responded. "Look, I want an administration to look -- and there's plenty of qualified, there's plenty of women with the experience and with the capability of being president tomorrow. And I think it's important that we begin to have my administration, God-willing, is going to look like America and I genuinely mean that. Not just vice president but making sure that we have a Supreme Court, we have a cabinet, we have a White House that looks like the country. And I think it really matters."

Biden continued: "And so I think it's really important -- and there's plenty of qualified people who have the experience and background who are women and are ready to be president on day one. And I'm gonna stick with that."

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Back in March, Biden declared during a Democratic debate that he would select a woman as his running mate.

"I would pick a woman to be my vice president," Biden said at the time, while also committing to appoint the first black woman to the Supreme Court.

Some on his shortlist include former 2020 rivals Sens. Kamala Harris, D-Calif.; Amy Klobuchar, D-Minn., and Elizabeth Warren, D-Mass., as well as Michigan Gov. Gretchen Whitmer and former Georgia gubernatorial candidate Stacey Abrams.

Fox News' Paul Steinhauser and Allie Raffa contributed to this report.