The message, delivered to senior members of the so-called Syrian National Coalition at a meeting of the anti-Assad Friends of Syria alliance in London last week, was prompted by rise of al-Qaeda and other terrorist groups, and their takeover of a border crossing and arms depots near Turkey belonging to the so-called Free Syrian Army, the sources told Reuters.
"Our Western friends made it clear in London that Assad cannot be allowed to go now because they think chaos and an extremist militant takeover would ensue," said one senior member of the Coalition who is close to officials from Saudi Arabia.
Noting the possibility of Assad holding a presidential election when his term formally ends next year, the Coalition member added: "Some do not even seem to mind if he runs again next year."
The shift in Western priorities, particularly the United States and Britain, from removing Assad towards combating extremist militants is causing divisions within international powers backing the nearly three-year-old revolt, according to diplomats and senior members of the coalition.
Like US President Barack Obama's rejection of air strikes against Syria in September after he accused army forces of using poison gas, such a diplomatic compromise on a transition could narrow Western differences with Russia, which has blocked United Nations action against the Syrian government, but also widen a gap in approach with the militants' allies in the Middle East.
Unlike in Libya in 2011, the West has ruled out military intervention, leaving militant groups including al-Qaeda affiliates to emerge as the most formidable rebel force, raising alarm among Washington and its allies that Syria, which borders Israel and Iraq, has become a Centre for global terrorism.
Saudi Arabia and Turkey, however, believe that tackling militants is less of a priority, with Riyadh in particular furious at what it considers US appeasement of Assad and his Iranian backers. Riyadh sent only a junior diplomat to the Friends of Syria meeting in London.
Also signaling differences with Washington, opposition militants in Syria have said that Turkey has let a weapons consignment cross into Syria to the Islamic Front, the rebel group that overran the Bab al-Hawa border crossing last week, seizing arms and Western equipment supplied to FSA.
Peace talks are due to start in Switzerland on January 22.
The Coalition has agreed to go to the talks while insisting on Assad's immediate removal, but a Middle East diplomat said opposition leaders should be "more creative" in their tactics - notably in agreeing to take part in transitional arrangements that would leave Assad's fellow Alawites in key positions.
"For Geneva to produce an arrangement acceptable to the United States and Russia, the opposition would have to accept taking part in a transitional administration with a strong Alawite presence," the diplomat said. "Assad may or may not stay as president but at least he will have diminished powers.
"If the opposition rejects such a deal, they will lose most of the West and only have Saudi Arabia, Libya and Turkey left on their side."
A second member of the Syrian opposition, who is in touch with US officials, said Washington and Russia appeared to be working in tandem on a transitional framework in which Alawites would retain their dominant role in the army and security apparatus to assure their community against retribution and to rally a unified fight against al-Qaeda with moderate rebel brigades, who would be invited to join a restructured military.
A senior Western official said that Russia and the United States have discussed which government officials - and up to what level of seniority - could be retained in a transitional phase but that they had not agreed any fixed blueprint.
BA/BA