Riyadh said last week that a suspected Al Qaida militant had claimed responsibility for kidnapping the diplomat, Abdullah Al Khalidi, and demanded the release of militants in Saudi prisons.
He threatened in a call to the Saudi embassy in Sana’a to kill the diplomat unless his demands were met.
Shaikh Tareq Al Fadli, a tribal head in Abyan and a prominent leader of Yemen’s southern separatist movement, said he had been mediating with the kidnappers for Khaladi’s release.
"Things are going well… The man is fine, he is in good health," Fadli told Reuters, adding that he would be released "within the coming hours".
Khalidi, the Saudi deputy consul in the southern Yemen port city of Aden, was seized outside his residence on March 28.
A Saudi spokesman said the Al Qaida caller had been identified as Mishaal Al Shodoukhi, who was named on a list of fugitive Al Qaida militants by Saudi authorities in 2009.
Shodoukhi said his group would "prepare the knives" unless their demands were met, an official Saudi spokesman said, and threatened further attacks, including an embassy bombing and the assassination of a Saudi prince.
Riyadh, which has substantial influence among Yemeni tribes, rejected any negotiations with Al Qaida for the release of Khalidi and vowed to do all it could to free him.
The political turmoil in Yemen has strengthened Islamist insurgents in the country, who have taken over some cities in the south of the impoverished Arabian Peninsula state.
They are allied with a regional wing of Al Qaida that has sworn to bring down neighbouring Saudi Arabia’s ruling family.
