The discussions came as pro-democracy protesters again filled the streets of Katmandu and the seven-party opposition alliance prepared for an anti-monarchy rally on Tuesday that they vowed would be the biggest in Nepal's history.
Countries with strong ties to Nepal were encouraging King Gyanendra to give the opposition alliance what it is demanding, including the reinstatement of Parliament, and an apology for 14 demonstrators killed by security forces over three weeks of protests, said a diplomat, speaking on condition of anonymity because of the sensitivity of the discussions.
The diplomat said the opposition was split on the potential deal.
King to speak
Late on Monday, state radio reported that Gyanendra would make an announcement after days of silence.
Another person familiar with the discussions, also speaking on condition of anonymity, confirmed that negotiations were under way, and said India was among the countries in the forefront of the talks.
Protests have rocked Katmandu for nearly three weeks, and police repeatedly have clashed with demonstrators demanding Gyanendra relinquish the absolute power he seized 14 months ago when he dismissed an interim government, saying he needed to bring order to the country's chaotic political situation and crush a Maoist insurgency.
Riot police patrol during day-time
curfew in Kathmandu
The protests and general strike have paralyzed the country, with the capital locked down by repeated curfews, roads blocked by protesters and food and fuel increasingly scarce.
Protesters, police clash
On Monday, pro-democracy protesters again faced off against security forces in Kathmandu.
Police fired tear gas and rubber bullets at a group of protesters, and at least seven were injured, independent Kantipur radio reported.
Protests were also held in dozens of towns across Nepal, according to local news reports, with demonstrators blocking roads with barricades of chopped-down trees and burning tires.
In the western resort town of Pokhara, 10,000 protesters marched through the heart of the town, including many government workers.
An injured suspected government
spy is led away by protesters
Amid the increasing chaos, the U.S. State Department on Monday ordered all non-emergency embassy staff and family members to leave Nepal, according to an embassy spokesman, Robert Hugins. He said about half of the mission's staff would leave.
Ambassador James F. Moriarty also recommended that all Americans in Nepal should consider leaving "because of the uncertain security conditions", an embassy statement said. China, Australia and Denmark are among the countries that have also warned people against traveling to the kingdom.