The plan from the Gulf Co-operation Council (GCC) would see Mr Saleh quit within a month of signing the agreement and hand over to his vice-president.
Mr Saleh's ruling party has said it will respond within 24 hours.
At least 120 people have died in weeks of protests demanding the end of Mr Saleh's 32-year rule.
The GCC previously offered Mr Saleh a proposal in which he was asked to stand down, but which did not outline a timetable. The proposal was rejected.
The revised plan also suggests Mr Saleh appoint an opposition leader to run a new cabinet that would prepare for presidential elections two months later.
Under the plan, half the members of a new unity cabinet would belong to the ruling party, while 40% would be from the opposition party. The other 10% would be from other political groups.
It also offers immunity from prosecution to Mr Saleh, his family and aides.
Aides to Mr Saleh said he seemed poised to accept the initiative, according to Reuters news agency.
"We welcome this new initiative and we will deal with it positively," an official said, after Mr Saleh met GCC Secretary General Abdullatif al-Zayani on Thursday.
But the opposition rejected the plan, saying they did not trust the government to keep to the conditions, and reiterated their demand for the president to leave immediately.
"This speech is to raise spirits, but it's no longer logical because the people have had their say - they say an immediate departure is necessary," said Sultan al-Atwani, the leader of the Nasserist party, which is part of the opposition coalition.
Meanwhile, clashes took place between troops and gunmen in the southern province of Lahj, a security source told Reuters.
On Wednesday, UN Security Council members called for restraint and dialogue between protesters and authorities in Yemen, but talks on the crisis ended without agreement.
The Yemeni leader, who has been in power for more than three decades, has said he is willing to hand over power but only to "safe hands".
Mr Saleh's weak central government already has little control beyond the capital.
In recent years it has struggled to confront an armed rebellion in the north and a secessionist movement in the south.
A grouping of Gulf states has presented Yemeni President Ali Abdullah Saleh with a new proposal in an attempt to end the country's political crisis.