Movie rights to the musical reportedly are owned by Universal, and Hooper is hoping to partner with the Les Misérables production company Working Title on the project.
Quoting unnamed "sources close to Hooper," the Sun said filming could start this year.
A Broadway revival of Cats is scheduled for this summer. The show enjoyed a successful London revival in 2014 as well.
Lloyd Webber revealed in 2012 that "serious" talks were underway to bring his long-running 1981 hit musical to the screen.
"There is considerable talk at last about Cats being made into a movie so it gives me a chance to think about the material and how that can happen," Lloyd Webber told Reuters at the time.
The production was previously filmed live on stage and released in 2000.
Based on T.S. Eliot's "Old Possum’s Book of Practical Cats," the musical became an international phenomenon and has continuously toured the U.S. for 30 years in various union and non-union productions. In 1991 Cats became the longest-running continuous tour in U.S. history. Cats produced the stand-out single "Memory."
Cats opened on Broadway at the Winter Garden Theatre Oct. 7, 1982, where it ran for 7,485 performances before closing Sept. 10, 2000. It held the title of Broadway's longest-running musical, but was surpassed by Lloyd Webber's other hit, The Phantom of the Opera, which currently holds the title. Cats won seven Tony Awards including Best Musical, Best Book of a Musical, Best Lighting and Best Costumes.