Both NBCUniversal and representatives for the couple declined to comment when contacted by Variety.
Sources also revealed that Meghan "has absolutely no plans to act" in the project.
Since returning to Hollywood, Meghan lent her voice as a narrator for Elephant, a Disney+ docuseries that premiered in April. The film benefits Elephants Without Borders, an organisation that protects elephants living in Botswana.
The opportunity came about after Meghan was spotted having a conversation with Disney chairman Bob Iger at the London premiere of The Lion King last summer.
Representatives for Disney also declined to comment when asked if Harry and Meghan had pitched their latest idea to their networks.
Variety also noted that it is currently unknown if Harry or Meghan have met with Netflix or Apple to pitch the idea.
The couple currently reside in Meghan's native California with their son Archie after stepping back as senior members of the royal family and instead work independently.