JERUSALEM — With just days left for Israel’s parliament to find a solution to the country’s ongoing political deadlock, there have been a flurry of proposals that lawmakers hope will prevent a third election in less than a year.

After elections in April and September and months of haggling and negotiating by the largest parties to form a ruling coalition in the Knesset, the country is no closer to a new government, whether led by the ruling Likud party of Prime Minister Benjamin Netanyahu or the Blue and White faction of former military chief Benny Gantz.

Add to that the criminal indictments issued against Netanyahu last month by the country’s attorney general, which have given rise to the question of whether he would be legally allowed to try forming a government if his party were successful in gaining a clear majority in a third vote. (Most polls suggest the outcome would be similar to the April and September elections.)

There are still hopes that another election can be avoided. Here are some of the proposals to break the deadlock:

A faceoff between Netanyahu and Gantz: On Saturday, Netanyahu said that after trying everything to form a unity government with Gantz and Blue and White, including sharing sensitive security information, there should be a “direct election for prime minister between myself and Gantz.”

“Let the people decide and no one else,” he said in a video.

A poll published Friday by Israel’s Channel 12 News showed Netanyahu still holding the lead, 39 percent to 37 percent, over Gantz on the question of who is best suited to be Israel’s prime minister.

Why it probably wouldn’t work: With no functioning parliament for nearly a year and without a clear majority in that parliament, the chances of ­Netanyahu and his supporters being able to pass legislation to overhaul the election process is very slim.

A direct election for prime minister is not a new concept. Israel experimented with it briefly in the 1990s — it’s how Netanyahu was first elected, in 1996 — but, even then, the task of forming a coalition proved extremely difficult. If it happened now, with the country even more polarized, some say, it would be even harder.

Not Netanyahu, not Gantz — but someone else: On Saturday, a Labor Party lawmaker said he was planning to gather signatures from 61 members of the Knesset in the days before it is dissolved Wednesday to recommend that Speaker Yuli Edelstein have a try at forming the next government.

“I really hope and believe that, if the president tasks him with this, he’ll make the right choice,” Omer Barlev said, according to Israeli media reports.

Why it probably wouldn’t work: Edelstein, who ranks second in the Likud party after Netanyahu, has in recent weeks become the central figure mediating between the two sides, but he has not explicitly said he would not take on such a role.

Following Barlev’s comments, Edelstein said, “The only way to prevent unnecessary and costly elections is through a unity government with a rotation between Netanyahu and Gantz.”

Even if a majority of Knesset members recommended Edelstein try forming a government, it would be a challenge. Under the law, he would have only 14 days to hammer out complicated and potentially explosive coalition deals between already bickering factions.

Rotating leaders: After the September election, President Reuven Rivlin proposed allowing Netanyahu to continue as prime minister for the next year, handing over to Gantz for two years, and then, if he cleared up his legal mess, he could return for the final year.

Netanyahu said last week he would be willing to shorten the initial term, handing over to Gantz in five or six months.

Why it probably wouldn’t work: Blue and White is made up of three separate parties with four prominent leaders. They have said that they would agree to such a rotation in principle, but they’re wary of Netanyahu’s promises.

They’ve also promised not to serve with a prime minister facing indictment and say that, as leader of the biggest party, Gantz should be first in the rotation, so they have refrained from accepting the proposal.

Gantz called on Netanyahu last week to make “life compromises.”

“Blue and White won the election, but we are prepared to allow for a rotation between us as part of a unity government,” he said. “I will serve for a two-year term, during which time you can remain at the helm of Likud and take care of your affairs. I assure you that we can find the correct status for your unique situation. This will allow you to return, should your name be cleared.”

Likud replaces its leader: Netanyahu’s ruling Likud is fiercely proud of being a democratic party loyal to its leader. A new leader can be chosen only through direct internal primaries. The last primaries were in 2014; Netanyahu won 75 percent of the vote.

The party’s central committee met on Sunday to decide whether to hold new primaries for leadership. Gideon Saar, a popular former minister and member of parliament, has said he intends to challenge Netanyahu.

Why it probably wouldn’t work: Saar called for primaries two weeks ago, saying the only way for Likud to stay in power was for him to take over and negotiate a unity government with Blue and White.

The party voted Sunday not to hold primaries for the party’s list, saying it would decide on a vote for leadership when it became clear there would be a third election.