Al Ahli have already made approaches for Harry Redknapp, Marcello Lippi and Sam Allardyce and have now turned to free agent Hughes.
Open to offers: Former Manchester City manager Mark Hughes
However, the former Manchester City boss remains in the frame to replace Roy Hodgson at Fulham, who seems destined for Liverpool.
After yesterday's result he may also find himself approached by England this week.
Hughes is definitely interested in Al Ahli's proposal but would prefer a return to the Premier League.
Sven Goran Eriksson and Alan Curbishley are also in the running for the Fulham job.
Sportsmail revealed Al Ahli's move for Redknapp last month which was closely followed by their signing of Italy captain Fabio Cannavaro.
Nigel de Jong claims Dutch success has its influence in the Premier LeagueArsenal, City and Chelsea set for Ozil battle as Barca block route to England