Maw of Malmortius (95 AD at 30% health)
Bloodthirster (80 AD)
Essense Reaver (80 AD)
Infinity Edge (80 AD)
Mercurial Scimitar (80 AD)
Sword of the Occult (110 AD)
Take Brute Force, Martial Mastery, and Warlord in the offensive tree.
15 AD from runes.
So I think that's (15+(4+10) + 95 + 80 + 80 + 80 + 80 + 110)*1.05 = 581.7, excluding any ability bonuses.
Add dragon buff and dragon buffs: (581.7 + 40)* 1.06 = 659 AD
Including ability bonuses, Malphite is probably the champion who can reach the highest AD since his W gives him a 40% bonus on his total AD value.
(119 + 659)*1.4 = 1089.2 AD
I might be wrong, but I think that's probably the highest you can get for AD, though Homeguard + Mobility Boots Hecarim with many speed boosts from allies might be able to achieve higher AD.