Anthony has kept out of the public eye since she was acquitted last summer in Orlando, Fla., of killing her 2-year-old daughter, Caylee. She was convicted of lying to police but was freed from jail July 17.
The Reporter said it had heard from several sources that Scott Sternberg, owner of Scott Sternberg Productions in Los Angeles, has been seeking an outlet for an interview. Sternberg's terms are said to be that the network can choose the interviewer and his company will be the co-producer.
Several cable networks have rejected the offer, the sources said. Discovery Networks and A&E Networks told the Reporter they turned Sternberg down.
Anthony would almost certainly be a huge ratings draw. HLN's broadcast of the trial attracted a record number of viewers with more than 5 million watching the verdict.
But cable industry insiders say paying for an interview with Anthony would anger viewers and would likely lose money.
"It will get very good ratings," one told the Reporter. "But who would want to put their ads in that kind of show?"