Allen owns Allen Media Group, which has a portfolio of cable networks including Atlanta-based Weather Channel network, the Grio streaming app, a film and TV production company and 27 broadcast TV stations.
The Journal said Skydance Media and Warner Bros. Discovery, which owns CNN, have also kicked the tires.
Paramount Global has not responded to media inquiries seeking comment.
National Amusements, the movie theater company which controls Paramount, has been seeking potential buyers in recent months, the Journal said, as the media world tries to figure out how to shift from a focus on TV to streaming.
Paramount Global owns broadcast network CBS and several cable networks including BET, VH1, Nickelodeon and Comedy Central as well as Paramount+, which has about 63 million global subscribers, ranking fifth globally but far behind leading streamer Netflix.
Allen last year jumped into the bidding for a majority stake in Paramount’s BET assets, which Paramount briefly considered spinning off, offering $3 billion.
Atlanta-based Tyler Perry also put in an offer. Paramount ended up nixing that idea.
Perry later told Bloomberg at a summit in Atlanta that he “was disappointed about it for a number of reasons. The way it happened was disrespectful in a lot of ways.”