Saudi Arabia is considering a proposal by Yemen's Iran-aligned Houthi movement for some form of ceasefire which, if agreed, could bolster UN efforts to end a devastating war tarnishing Riyadh's reputation.
The Houthis offered two weeks ago to stop aiming missile and drone attacks at Saudi Arabia if the western-backed coalition led by Riyadh does the same, as a step to what a Houthi leader called a "comprehensive national reconciliation".
There was no immediate Saudi acceptance or rejection of the Houthi offer. But Riyadh this week welcomed the move, and three diplomatic and two other sources familiar with the matter told Reuters the kingdom is seriously considering some form of ceasefire to try to de-escalate the conflict.
Yemen's 4-1/2-year-old war, which the United Nations has described as the world's worst humanitarian disaster, has pushed what was already one of the poorest Arab states to the brink of famine.
UN-mediated efforts to resolve the complex war have been tortuous, with cross-border strikes by both sides a central grievance for the Houthis and Saudi Arabia, which borders Yemen.
Saudi's Western allies, including those that provide arms and intelligence to the coalition, have been pressing for an end to the war, which has killed tens of thousands.
Two of the sources said Saudi airstrikes on Houthi territory had decreased significantly, and that there were reasons to be optimistic about some sort of deal emerging soon.
Saudi Arabia's vice minister of defence, Prince Khalid bin Salman, said on Thursday on Twitter the kingdom viewed the Houthi truce offer "positively", echoing comments earlier this week by Saudi Crown Prince and de-facto ruler Muhammad bin Salman, also known as MbS.
The Houthi proposal was a "positive step to push for more serious and active political dialogue ... Today we open all initiatives for a political solution in Yemen. We hope this happens today rather than tomorrow," MbS said in a CBS television interview.
In July the United Arab Emirates - a leading partner in the Saudi-led coalition and the main ground fighting force - announced a drawdown of its presence in Yemen, signalling a pull-back from the anti-Houthi fight.
At that time diplomatic and military efforts to end the war was going nowhere and growing US-Iran tensions were threatening the UAE's security closer to home.
Riyadh vowed to continue to confront the Houthis but, two months later and having lost their main ground partner, Riyadh appears now to be more open to options other than fighting.
A regional official familiar with the matter said the Saudis are considering the Houthi offer, which western diplomats are using to convince Riyadh to change tack.
"They seem very open to it," the source said.
A senior military source in Yemen on the Houthi side said that Saudi had "opened communication" with the head of the Houthi political office, Mahdi al-Mashat, via a third party, but no deal had been reached.
This offer involved a partial ceasefire in certain areas, the source said. Two diplomatic sources and the source familiar with the matter also said a partial ceasefire was on the table.
But Houthi officials have said a partial deal is unacceptable. "What is required is a complete cessation of airstrikes in all of Yemen and an end to the siege on the Yemeni people," the Houthi information minister said.
"MbS wants to get out of Yemen so we have to find a way for him to get out while saving face," a European diplomat said.
Another diplomat said Saudi Arabia agreeing to halt airstrikes would effectively mean the war ends, as Saudi Arabia does not have extensive ground capabilities.
There are also signs the international community is coming together to encourage Riyadh to engage with the Houthis.
Eight countries, including the five permanent members of the UN Security Council - Britain, France, the United States, China and Russia - met on the sidelines of the UN General Assembly last week in New York and said the Houthi offer was "an important first step towards de-escalation which will need to be followed with positive action on the ground by the Houthis as well as restraint by the coalition".
The Houthis have threatened that if their peace initiatives are not heeded, more cross-border attacks might follow.
"For the sake of peace, we postponed many strategic strikes that are no less than Aramco's size and impact," al-Mashat said, referring to a strike last month on Saudi oil infrastructure claimed by the Houthis, although Washington and Riyadh said Iran was responsible and the attacks did not come from Yemen.
Although the war has its roots in internal conflict lines pre-dating the Houthi ousting of President Abd-Rabbu Mansour Hadi in Sanaa in 2014, it is now viewed regionally as a proxy fight between Saudi Arabia and its Shi'ite Muslim rival Iran.
A key Saudi motive has been to avoid having a hostile Iran-backed force on its borders like Lebanon's heavily-armed Hezbollah, or Iran-backed militias in Iraq. Riyadh said twice this week it wants the Houthis to distance themselves from Iran.
"If Iran stops its support of the Houthi militia, the political solution will be much easier," MbS told CBS.
"The Saudis are very open to (the Houthi offer) as they are willing to use it to make their case that Iran is the problem, not the Houthis," the regional official familiar with the matter said.
Iran denies arming the Houthis, but says it advises their forces. Iranian armed forces chief Major General Mohammad Baqeri said on Thursday Iran would "stand to the end with the Yemeni people until they get rid of this (coalition) aggression".