"Alejandro Sabella excused himself from coaching the Saudi national team in the coming period," Saudi Football Association official Adnan Al Muaebed told Emirati paper Sport360.
"We went through gruelling negations with Sabella in order to persuade him but he declined the offer."
Sport360 added that Sabella's agent had said the experienced coach had not wanted to work in the Middle East.
Saudi Arabia FA president Ahmed Eid told BBC World Football on Friday they had wanted a South American coach to take charge and identified Sabella and Chile's Copa America-winning coach Jorge Sampaoli as candidates they were speaking with.
Former Chile and Argentina coach Marcelo Bielsa is another who has long been linked with the vacancy.
Saudi Arabia, who have qualified for four World Cups, have been without a permanent head coach since unpopular Spaniard Juan Ramon Lopez Caro was sacked following defeat at home to Qatar in the final of the Gulf Cup in December.
Romanian Cosmin Olaroiu took charge for the Asian Cup in January but the Green Falcons suffered a disappointing group stage exit in Australia.
The Saudis kicked off their 2018 World Cup qualifying campaign under an interim coach with a narrow 3-2 win over Palestine in June and face further Group A matches at home to East Timor and away to Malaysia next month.
(Writing by Patrick Johnston in Singapore; editing by Sudipto Ganguly)
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