Nafziger's Army Lists provides some information (see link). For example, in 1801 the Ottoman forces are given as:

Corps of Capitan Pasha [landed from the Ottoman Fleet]
- Albanians and Janissaires (6,000)
Army of the Visier [advanced overland]
- English Gunners and Engineers (500!) [Nafziger is in error - the British mission was 76 strong when established in late-1798, but was less than 50 by this time]
- Advanced Guard of Aboumarak, Pasha of Jersulam (2,000 infantry & 1,500 cavalry)
- Corps of Abraham, Pasha of Alep (3,000 cavalry & 2,000 cavalry)
- Troops of the Pashas of Damas, Ismael and Taher Pasha (3,000 infantry & 5,000 cavalry)
- Jannissaires and Guards of the Visir (3,000 infantry & 1,000 cavalry)
- Mameluks of Abraham (800 cavalry) [frpm Egypt]

More information can be gleaned from works such as William Wittman, 'Travels in Turkey, Asia-Minor, Syria, and across the Desert into Egypt during the Years 1799, 1800, and 1801 in Company with the Turkish Army and the British Military Mission', London 1803 (available Google Books), but I doubt even the Visier truly knew the composition of his army!

Regards,

David