But Bessam Dade, political adviser to the rebel Free Syrian Army, said the dissidents would approve of such a plan only if Syrian President Bashar al-Assad is not granted immunity from prosecution, Turkey's TRT news agency said.
Turkish Foreign Minister Ahmet Davutoglu pitched the idea, saying the Syrian vice president is not to blame for the mass bloodshed in the country.
"Farouq al-Sharaa, with a reasonable and conscientious approach, was not a part of recent events and did not partake in the massacres. And perhaps there is no one that knows the system better than Farouq al-Sharaa," Davutoglu told TRT, according to the Turkish Anadolu Agency.
George Sabra, a spokesman for the Syrian National Council, said members of the opposition group will meet in Qatar later this month and will discuss whether the Syrian opposition would accept the proposal.
"But first we need to know what will be the road map that such a transition will be based on," Sabra told CNN. "Whether it is al-Sharaa or anyone else, we need to know first what will this person do, and how he or she will push to get Syria out of this quagmire."
In August, a spokesman for the Free Syrian Army said that al-Sharaa had defected from the government and that rebels were trying to help him flee to Jordan. But al-Sharaa later resurfaced at an official meeting in Damascus.
He has not been seen publicly since, not even when al-Assad made a rare public appearance Saturday and was greeted by other Syrian officials.
On the ground: Rebels say they're close to seizing a military camp
In their quest to wrest control of land near the Turkish border, Syrian rebels stationed outside a military camp in Tal Abyad said they had destroyed three tanks by Monday morning.
"We feel very strongly we will take (the camp) over in the next few hours," rebel fighter Abu Abdallah told CNN.
Government forces have been shelling the surrounding area -- and firing mortar rounds that fell into Turkey -- from the Tal Abyad camp, said Abdallah and Ayham Khalaf, a witness and activist.
But Syrian state media reported that security forces had destroyed two vehicles and eliminated a number of terrorists during their attack.
If opposition fighters take over the military camp, Abdallah said, rebels will control an area that extends 45 kilometers (28 miles) south of the border of Turkey -- a country that has been sympathetic to Syria's opposition movement.
Also Monday, Abdel Basset Sayda, the head of the Syrian National Council, entered Syria and met with leaders of the rebel fighting force in Idlib province.
They talked about how the occupation of Homs could be broken and civilian issues, a spokesman for the council said.
World reaction: U.S. presidential candidate supports arming rebels
U.S. Republican presidential candidate Mitt Romney is expected to announce his support of Syrian opposition members in a foreign policy speech Monday.
"In Syria, I will work with our partners to identify and organize those members of the opposition who share our values and ensure they obtain the arms they need to defeat Assad's tanks, helicopters and fighter jets," according to excerpts from Romney's prepared speech. The remarks did not say whether the United States itself should arm the rebels.
"Iran is sending arms to Assad because they know his downfall would be a strategic defeat for them. We should be working no less vigorously with our international partners to support the many Syrians who would deliver that defeat to Iran -- rather than sitting on the sidelines."
Romney is running against President Barack Obama, who has not explicitly called for providing arms to Syrian rebels. The United States is helping Qatar and Saudi Arabia, which are arming the opposition, decide which rebels should receive weapons.