I feel like you would need s POD that significantly strengthens Byzantium defenses in anitolia in order to funnal the turks south towerd the Arabs instead as a easier target with any number of the "16 Great Turkish Empires"
en.m.wikipedia.org
(prehapse considering the terrain of the Fertile Cresent more attractive then mountainous anitolia) and place more priority on the middle east then otl during thier invasions and overtime lowering the native populations with invasions while resaturating the Fertile Cresent with the Turkish populations and customs brought by the various empires
As for a location, assuming a east to west invasion I feel like it's almost impossible for eygipt to fall to such a degree while keeping Damascus and Bagdad in arab hands so I think we can write them off (theoreticly they might exist as a frontline city under constant seidge but that's not a good location do to economic surpluses being consumed by defense and not cultural centers) so I would assume outside of mecca it might migrant west towerd northwest Africa and occupy a space similer to the Fatimide Calipate but now divorced from eygipt I would assume Tunis, Raqqada or Mahdia would develop into a arab cultural center (the entire north east of Tunisia might honestly becuse all 3 city's are clustered fairly close together and in close proximity to the emirate of Sicily if it survives)
Alternitivly assuming Islam is able to reestablish control over Iberia with the aid of refugee populations from the Fertile Cresent that somewhere in Central or Southern Spain might develop into the leading arab cultural center.
If a strong Islamic calipate can unite these regions west of Turkish eygipt I could see a western calipate claiming to be a succesor to Carthage as opposed to the otl Ottomans claiming to being the succesor of Eastern Rome with the right motivation.
As a side note a western arab calipate would be in a good position for colonization without having to worry about being bottled up in the mediteranian per OTL and without otl competition from Portugal and Spain due to them being part of the calipate then the lack of thier claims and competition would dramatically change up who fills this now empty space.