Representative Nancy Pelosi of California, the former speaker, recently told her colleagues in the California delegation that if President Biden were to end his campaign she would favor the “competitive” process of an open primary rather than an anointment of Vice President Kamala Harris as the new Democratic presidential nominee.

In one of the delegation’s weekly closed-door meetings earlier this month, a small group of members were discussing the party’s stressful state of affairs, in which Mr. Biden appears defiant in the face of concerns from lawmakers and leaders in his own party who want him to step aside.

Ms. Pelosi, who arrived late to the meeting, spoke up in response to questions from members. When asked about Mr. Biden, she said she did not think he could win, citing polling data, an assessment that she has shared privately with the president himself. Ms. Pelosi said that if he stayed on the ticket, Democrats would lose any shot they might have of winning back control of the House, according to three people familiar with the confidential conversation who insisted on anonymity to describe it.

Lawmakers in attendance then pressed her on what the landscape would look like if Mr. Biden ultimately decided to step aside under pressure. Ms Pelosi told them she favored a competitive process. Ms. Pelosi, according to a source familiar with her thinking, is a friend and fan of Ms. Harris, a former senator from California. But she believes even Ms. Harris would be strengthened to win the general election by going through a competitive process at the convention.

A second person briefed on Ms. Pelosi’s views, who also declined to be named discussing private conversations, said her desire for an open primary process is driven by polling data about who can win the election, and that she believes the Democratic Party has a deep bench of talent to draw from, including governors and senators in competitive states.

Ms. Pelosi’s comments at the meeting regarding her preference for an open primary were first reported by Politico.