Saleh is being treated in Riyadh for injuries and burns he sustained from a bomb attack on a mosque in his presidential compound in the capital Sanaa on Friday.
The source said that the president was “out of danger and responding to medical treatment satisfactorily.”
Yemeni Vice President Abdal-Rab Mansur Hadii, said Saleh intends to return within days.
Tens of thousands of anti-government protesters went to streets Sunday in several major provinces to celebrate Saleh’s departure.
Protesters also pressed for a swift power transfer after opponents vowed to prevent Saleh from returning.
Meanwhile, the Gulf Cooperation Council (GCC) said its proposed exit deal, by which Saleh would step down in return for immunity against prosecution, remained the “most suitable solution.”
“The council member-states could activate the proposal and follow up on its implementation if Yemeni parties agree on it,” said GCC Secretary General Abdullatif al-Zayani, whose mediation since April has stalled due to conditions imposed by Saleh.