The film will be a new adaptation of Chris Van Allsburg's original 1981 adventure book, reported Variety.
Schedules are still being worked out, as both Johnson and Hart are busy with their individual projects, but sources say things are moving toward a deal.
Johnson, 43, who is currently filming the "Baywatch" movie, is also starring on HBO series "Ballers". He's set to reprise his role in "Fast and Furious 8" this summer and film video game adaptation "Rampage" next.
The plan is to shoot "Jumanji" before the filming of "Ballers" season 3 starts.
"Jumanji" revolves around a 12-year-old bo, who becomes trapped in a board game in 1969 and is released 26 years later.
Jake Kasdan is directing from the script by Scott Rosenberg and Jeff Pinkner. The film will hit theaters July 28, 2017.