UN envoy Staffan de Mistura told Syria's opposition attending peace talks in Geneva that the proposal could end the "vicious cycle" of debate over a transitional period to end the war, a source told AFP on Saturday.
On the ground, tens of thousands of Syrians are at risk of being displaced as clashes between opposition and militants intensified in the country's north.
The fate of President Assad remains the key sticking point in the discussions involving the opposition High Negotiations Committee and a government delegation.
The HNC insists Assad must leave, but Damascus objects to that demand, saying elections are the only means that can gurantee his exit from power.
A HNC source told AFP on Saturday that the committee had rejected a proposal by de Mistura that would have seen Assad remain as president through a transitional period.
In exchange, the HNC would have been allowed to hand-pick three vice presidents, the source said on condition of anonymity because he was not authorised to speak to the press.
"But we categorically rejected the proposal," he said.
While the opposition insists on forming a "transitional governing body" without Assad, Damuscus says it wants to form a broader "unity government."