The 26-year-old singer will be directed by Lorene Scafaria, who will also write the script for the motion picture, which will be based on Lewis Carroll's novel Alice's Adventures in Wonderland.
Sources close to the project have told Variety that Carpenter first approached Universal about the movie in 2024.
And the project has since moved forward after Scafaria signed up to write and direct.
Carpenter will produce the movie alongside Marc Platt, through his Universal-based Marc Platt Productions, as well as Leslie Morgenstein and Elysa Koplovitz Dutton through Alloy Entertainment.
Sources also told The Hollywood Reporter that an Alice in Wonderland musical movie is a "passion project" for the pop megastar.
Carpenter is no stranger to the big screen, previously appearing in 2013 movie Horns - alongside Daniel Radcliffe - and more recently Tall Girl 2.
In May, producer Judy Craymer admitted she wanted the Espresso hitmaker to appear in Mamma Mia! 3.
Craymer told Deadline: "She'd be a goddess or some relation who would look very much like Meryl Streep."
Sabrina, 26, is known to be a huge fan of ABBA and has performed some of the legendary Swedish group's hits on her Short n' Sweet tour.
The producer came up with the idea for the 'Mamma Mia!' musical, which launched in London's West End back in 1999, and explained that she has a script ready to go for the third film.
Craymer said: "Well, we know what we want to do with the movie, and it will happen.
"And I mean, we brought together this amazing group of movie stars that were all connected through it, and huge friendships evolved."
The original Mamma Mia! film was released in 2008 and featured an all-star cast including Streep, Pierce Brosnan and Amanda Seyfried.
It was followed by the sequel Mamma Mia! Here We Go Again in 2018.
Seyfried has previously championed the idea of Carpenter playing her on-screen daughter in the third movie.
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