The British actors are said to be the frontrunners to play Snake Plissken in the recently announced project, to be produced by Die Hard's Joel Silver.
Kurt Russell played Snake in the original 1981 sci-fi action film, a war-hero-turned-criminal who has the chance to redeem himself by rescuing the president, who has been taken hostage by prison inmates.
StudioCanal has joined forces with Silver Pictures for the project, and they have put Hardy and Statham at the top of their wish list, according to the New York Daily News.
"Jason is the type of actor who has the physical attributes and screen presence to reprise Snake," a Hollywood source said.
"He has a proven track record as a leading man and would do a great job."
They added: "Tom was immense in The Dark Knight Rises and deserves to get a break in a top role. This could put him firmly in the A-list.
"StudioCanal wants to make sure they get one of the two men before the summer."
The new version could potentially be part of a trilogy of movies, which will begin with an origin movie in a similar vein to Rise of the Planet of the Apes.
Jeremy Renner, Gerard Butler and Josh Brolin were among the actors tipped to play Snake in a proposed remake by New Line Cinema, until the project was dropped in 2011.
Watch a trailer for the original Escape from New York below: