Nibras Islam, 22, who was killed on Saturday during a joint operation by Bangladesh security forces at the Holey Artisan Bakery where militants held several people hostage.
In his Facebook page, Islam claimed he had met Bollywood Kapoor.
"In a video clip posted in Facebook on June 8 last year, Nibras was seen shaking hands with Indian actress Shraddha Kapoor," the Daily Star newspaper said quoting an unidentified police detective.
"Shraddha Kapoor you beauty!! The moment she holds my hand," read the text accompanying the video.
Videos and photos from Islam's profile show him as a well-spoken, pleasant boy. His Twitter profile shows that he used to follow Shami Witness, an account linked to ISIS.