In rejecting the plan, Saleh Friday warned against an intervention by foreigners in the country's politics, CNN reported.
"We get our power and trust from the great Yemeni people and the constitution," Saleh said. "We will reject any new initiative from any country dealing with Yemen's current crisis. Our power comes from the great people of Yemen, not Qatar or anyone else."
The GCC is a political and economic umbrella organization whose members include the United Arab Emirates, Bahrain, Saudi Arabia, Oman, Qatar and Kuwait.
Thousands of anti-government protesters gathered in the capital of Sanaa Friday, calling for Saleh's ouster.
"Yemen is in favor of President Saleh, but he is willing to step down for the love of the people," said senior ruling party official Yasser Awadhi.