Maine Democrats are eyeing a late July convention for selecting a new Senate nominee to replace Graham Platner, who recently suspended his campaign under widespread pressure from party leaders and allies to bow out.

The Democrats are currently planning to hold county meetings to choose delegates next weekend and a state convention the weekend after that to pick a replacement for Mr. Platner after his campaign imploded this week.

The emerging plans, described by five people familiar with them, who spoke on the condition of anonymity to discuss private talks, have yet to be finalized or announced by the Maine Democratic Party and are subject to change. Officials in the state are trying to create a process to choose a Platner replacement by a July 27 deadline, a herculean task for a small state party.

Devon Murphy-Anderson, the Maine Democratic Party’s executive director, did not respond to messages Friday.

Since Mr. Platner’s announcement on Wednesday that he would suspend his campaign after a rape allegation, which he denies, Maine Democrats have discussed an array of possibilities of how to choose several hundred party delegates it has said will vote on his replacement.

The process is riddled with political hazards.

During a Thursday night meeting of the state’s 16 county Democratic Party leaders, officials discussed methods for choosing delegates to the state convention, according to two of the people familiar with the emerging plans.