Graham Platner can be replaced as the Democratic nominee for Senate in Maine if he withdraws from the race by next Monday, and state law would then give the state Democratic Party until July 27 to name a replacement.

Maine Democrats would be in uncharted terrain if Mr. Platner does exit the contest after a Politico report that he sexually assaulted a woman he had dated. He denied the allegation but said he was taking time to “reflect” on his political path forward.

Maine law does not dictate what process the state Democratic Party would use to replace Mr. Platner should he step aside, according to Kate McBrien, the chief of staff to Shenna Bellows, Maine’s secretary of state.

The chairman of the Maine Democratic Party, Charles Dingman, and other Maine Democratic Party leaders posted a statement on social media calling on Mr. Platner to quit the race. Mr. Dingman did not immediately respond to messages on Monday afternoon.

Top Maine Democratic Party officials have discussed possible plans to replace Mr. Platner on the ballot, with options including a pop-up convention on the weekend of July 25 to choose a nominee, or holding a statewide caucus to effectively redo the party’s primary election, according to two people who have talked with the officials and spoke on the condition of anonymity to discuss internal party conversations.

Officials have ruled out having the state party’s committee, which includes about 100 members, choose the nominee, the people said.

Mr. Platner won Maine’s Democratic primary for Senate last month after his top rival, Gov. Janet Mills, suspended her campaign weeks earlier, citing poor fund-raising. Ms. McBrien said she was unaware of any precedent in which a Maine candidate had won their primary and then withdrawn before the general election.

Should Mr. Platner withdraw by next Monday, the leading candidates to replace him could potentially include the Democrats who ran for governor and did not win the primary.

They include Ms. Bellows, Troy Jackson, a former president of the Maine Senate, and Nirav Shah, a former director of Maine’s public health agency. Jordan Wood, who lost a primary for a House district covering northern Maine, is also a potential candidate.

Ms. Mills is seen as less likely to be selected. She did not respond to messages on Monday.