Ahmad Moaz al-Khatib, the former head of the opposition National Coalition, said a deal could see Assad remain in power for a limited time, despite previous demands for his immediate resignation.
"It is in the Syrian people's interest for us to sit down together once and for all, and to find a way to save the people from this pain and suffering," Khatib told AFP.
He was speaking after visiting Assad's key backer Russia in early November as part of a small delegation of political and military opponents of the regime.
Khatib remains an influential opposition figure even though he resigned from his post as coalition chief in 2013.
Speaking to AFP by phone from Qatar, he said: "We want to solve the problem, because the problem now affects each and every Syrian... The regime is suffering, the opposition is suffering and the people are suffering."
Syria's war has killed more than 195,000 people and forced half the population to flee their homes.
The conflict began as an anti-Assad revolt in 2011, but protesters took up arms months after the regime unleashed a brutal crackdown on dissent.
The main opposition coalition held talks with Syria's government earlier this year.
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But they collapsed as the opposition demanded Assad's resignation, while the regime insisted the main focus of the negotiation should be on fighting "terrorism".
The Assad regime has systematically referred to all its opponents, armed and unarmed, as "terrorists".
Khatib said Tuesday that he was ready to accept a solution to the war that would temporarily keep Assad in power.
"Of course (Assad) has to leave," Khatib said. "But the idea that his mandate would finish on a given date, this idea could make sense."
He said he believed Russia might eventually join calls for Assad to quit if steps were taken to prepare the ground for a handover.
Khatib's talks in Moscow were followed by a visit last month by a high-level Syrian delegation led by Foreign Minister Walid Muallem who met President Vladimir Putin.
Syria's pro-regime daily Al-Watan said at the time the two sides "laid the initial vision for a political solution to the Syrian crisis", without providing details.
The National Coalition, which has been internationally recognised but lacks influence in Syria, has voiced scepticism about prospects for progress.