Bachchan, 73, has worked with Mehra in hits like "Zanjeer", "Muqaddar Ka Sikandar", "Namak Halaal" among others.
"With the 'greatest' Muhammed Ali at his home in LA. Prakash Mehra had wished to make film with him and me," he posted on Twitter along with a black-and-white picture of the trio.
Boxing icon Ali has died after a 32-year battle with Parkinson's disease.