"The Yemeni president will not return to Yemen," the official said, requesting anonymity.
"It has not been decided where he will stay," the official added, apparently suggesting that Saleh might eventually leave Saudi Arabia for another country.
The official did not specify whether the decision not to return home was taken by Saleh himself. But a Yemeni official promptly denied the claim.
"President Saleh will return in the coming few days," deputy foreign minister Abdo al-Janadi told AFP.
The veteran leader was flown to Riyadh on June 4 on board a Saudi medical aircraft, a day after he was wounded in a bomb explosion at a mosque inside his Sanaa presidential compound.
He has not been seen in public since the attack. Reports on the condition of Saleh's health have been sketchy, but Bahrain's King Hamad was reported to have called him yesterday, two days after Saudi King Abdullah had a phone conversation with him.
In Saleh's absence, his deputy Abdrabuh Mansur Hadi has been coming under intensive local and international pressure to heed the demands of protesters to set up an interim ruling council, which would prevent Saleh returning to power.