It is quite clear that the reason why Mahrez turned down the offer was because he was still in his best form in Europe and there was no way he would give up what he had achieved this season with Manchester City to go to Al-Ahli. It seems that Al-Ahli will continue to look for other European candidates who want to join and it might be quite difficult because they are also a promoted team for next season's SPL. Mourinho gave the right decision to reject Al-Ahli, we know Mourinho is still at the highest level to handle Europe's top teams and his choice to stay with Roma is proof that he will still try to bring titles to the capital team.
It seems, currently there is a Saudi trend. Al Nassr with Ronaldo, Al Ittihad with Karim Benzema and currently Al Hilal and Al Ahli are trying to bring in other stars. before Mahrez, it was also rumored that Aubameyang would be brought in by Al Ahli or Al Shabab. however, there has been no continuation regarding this rumor.
Now, Al-Ahli is trying to win over Riyad Mahrez. however, as quoted by Fabrizio Romano, any Saudi party interested in signing Riyad Mahrez received a clear message from Man City: an important fee will be required. a subsequent tweet, Saudi side Al Ahli interest in Riyad Mahrez, confirmed and concrete as they want to sign the Algerian star - but Manchester City have not been approached at this stage. Manchester City will need a consistent fee for Mahrez, no chance of letting him go for free.
Seems like this is a signal, that Manchester City could just let him go. however, I haven't tried to read the news that Mahrez has turned it down. it is possible, that the news is not true.
By the way, I'm pretty sure that Al Shabab, Al Hilal and Al Ahli, will be hunting for some European star players to add to the excitement of the Saudi Pro League competition.