The gossip site also suggested that the actor, who will be producing the project, wants to cast his daughter Sonam in the film.
"When he was in Los Angeles recently for the wrap-up party of his TV series 24, Anil met up with Disney officials to discuss the deal," a source revealed.
"It was his beti [daughter] Sonam who suggested that he remake the film. Just the paperwork needs to be signed. The film will start this year-end, once all the negotiations are complete."
Jodie Foster starred in the original Freaky Friday which was released in 1976, while Jamie Lee Curtis and Lindsay Lohan starred in the 2003 US remake.
Kapoor apparently wanted to cast Kirron Kher as the mother in the movie, but she is said to have turned down the role.
"Kirron has turned down the role citing date problems but relations between the Khers and the Kapoors have been strained, and that could well be the reason for this snub," the source added.
"The other names that the actor is toying with are Rekha and Shabana Azmi. The film will be directed by Priyadarshan."