Staffan de Mistura made the proposal for Assad to remain in office during a transitional period to the High Negotiations Committee -- the main Syrian opposition body -- during a meeting late Friday, the HNC source said.
"He proposed that President Bashar al-Assad would appoint three vice presidents that we choose, and that he would transfer his military and political prerogatives to them," the source said.
"Effectively, Assad would stay in a ceremonial position... But we categorically rejected the proposal."
The HNC and the government delegation are in Geneva for a fresh round of talks aimed at resolving Syria's five-year war.
The UN-backed effort has called for a political transition, a new constitution, and parliamentary and presidential elections by September 2017.
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Assad's ouster has been the key demand of Syria's opposition since the uprising broke out in March 2011, but Damascus says his departure is not on the table.
While the opposition insists on forming a "transitional governing body" without Assad, the regime says it wants to form a broader "unity government."
The HNC source said de Mistura had presented the idea as a way to end that "vicious cycle" of debate.
"This way, the president could transfer his prerogatives based on the current constitution, which does not include the formation of a transitional governing body," the source said.
According to him, de Mistura told the HNC committee that the proposal "was not his personal view... but that he hoped to hear our thoughts".
On Friday, HNC spokesman Salem al-Meslet told AFP that Syria's opposition would be willing to cooperate with regime "diplomats and technocrats" in a transition period.
He insisted that there would be no role for Assad or anyone who had played a central role in the civil war, which has killed 270,000 people and displaced millions.