JOIN USAbu Bakr al-Kurbi told the kingdom's Al-Watan daily that Saleh will remain in the kingdom for medical tests, after Wednesday's historic agreement to transfer powers to his deputy.
"No specific date has been set for his departure," from Saudi Arabia, Kurbi was quoted as saying.
Saleh's return to Yemen "depends on the (medical) results which will determine if he will be treated in the kingdom or in the United States.
"If the results are reassuring, he will return to Yemen," Kurbi added.
On Wednesday, UN chief Ban Ki-moon said that Saleh would seek medical treatment in New York after signing the deal brokered by the six-nation Gulf Cooperation Council which effectively ended his 33-year rule.
"He told me clearly that he will hand over all powers," Ban told reporters at the UN headquarters as Saleh signed the exit deal in the Saudi capital the same day.
"He told me that he would come to New York after signing the agreement to have medical treatment," Ban added, giving details of a telephone conversation on Tuesday.
Saleh has already been treated in Saudi Arabia for wounds sustained in an attack on his palace on June 3, and it was not known why the 69-year-old president would consult doctors in the United States.
Under the deal, Saleh hands over, with immediate effect, all "necessary constitutional powers" to Vice President Abdrabuh Mansur Hadi and holds office on an honorary basis only for the coming 90 days.