Sir Ian, 76, is in the country as a part of Shakespeare Lives on Film, a global programme to celebrate the Bard's works and his influence on culture, education and society, coinciding with his 400th death anniversary.
Aamir, dressed in a shirt and pants was photographed with Sir Ian.
Sir Ian and Aamir were delighted to meet each other. They happily posed for the shutterbugs.
Aamir is also conducting a session with Sir Ian.
Mumbai is the first stop of Sir Ian's global tour as the BFI's ambassador for Shakespeare Lives on Film.