Al-Ahli will host Al-Nassr on 20 November, at the Al-Inma Stadium in Jeddah, in a match postponed from the ninth round of the Roshn League.
Saudi newspaper "Arriyadiyah" report that the Al-Ahli board are currently searching for a suitable way to end their contractual relationship with Bosić before the anticipated Clasico against traditional rivals Al-Nassr.
For now, though, the Dutchman looks set to remain in the dugout for that Clasico, with the departure procedures yet to be finalised.
Al-Ahli's fans had already launched a fierce social media campaign under the banner "Bosić's departure is our demand", calling on the club to sack the Dutch coach amid a run of poor results.
That campaign only grew louder after the 6-1 thrashing by Al-Shabab in the twelfth round of the Saudi Roshn League.
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Bosić took the Al-Ahli job last August, succeeding German Matthias Jaissle, who left suddenly to take charge of Newcastle United.
Since arriving at the Jeddah club, Bosić has overseen 18 matches, winning 11, drawing two and losing five.
Al-Ahli sit sixth in the Saudi League on 21 points, picked up from 7 wins and 4 defeats, a full nine points behind leaders Al-Hilal.
In the AFC Champions League Elite, Al-Ahli occupy sixth place in the West Group on 8 points, taken from two wins and two draws, still unbeaten.
Al-Ahli have already come through the King's Cup round of 32, beating Al-Anwar 2-1. They now prepare to face Al-Ula on Monday 11 January, at the Prince Mohammed bin Abdulaziz Stadium in Medina, in the round of 16.
Kuwait awaits too. Al-Ahli will contest the Saudi Super Cup there, meeting Al-Qadsiah on 20 December, and should they qualify, they will face the winner of Al-Nassr and Al-Khaleej in the final on the 23rd.
Al-Ahli began their preparations for the Al-Nassr clash the day before yesterday, Wednesday, without five players away on international duty during the current break, chief among them Saudi pair Firas Al-Buraikan and Ziyad Al-Johani.
Also on that list are Portuguese winger Francisco Trincão, Turkish defender Merih Demiral and French midfielder Valentin Atangana.