Directed by Hrishikesh Mukherjee, the 1982 film starred Amitabh Bachchan, Rakhee Gulzar and Vinod Mehra.
A source told the Hindustan Times: "Karan Johar wants to remake Bemisal. We're not sure whether or not he will direct the movie himself, but he has been thinking about remaking it at some point.
"Karan has been thinking about casting Aishwarya Rai Bachchan to play Rakhee's character from the original. In fact, he is in talks with Aishwarya. She has been away from films for a while and we haven't heard of a confirmation yet from her end. But if all goes well, we will hopefully see her return to the big screen with this."
The Raavan star has not worked with Johar in a film before.
It was recently reported that Rai Bachchan was to star in a remake of Rebecca, but the actress has not confirmed any film roles since giving birth to her first child last year.
The former Miss World has said that her priorities have changed since becoming a mother.