The letter is not meant for publication, the report said.
Fox News is continuing to pay Carlson and says that his contract keeps his content exclusive to Fox through December 31, 2024, the report added.
Carlson has released two episodes of his "Tucker on Twitter" show, a 10-minute monologue in which the conservative political commentator discusses latest developments. The host said that his Twitter videos are protected under the First Amendment and accuses Fox of committing material breaches of his contract.
In late April, Fox News agreed to part ways with the host of its highest-rated news show. Reports suggest Carlson was let go due to his coverage of controversial topics — ranging from the January 6 events at the US Capitol and the COVID-19 measures to the US involvement in the Ukraine conflict — while others have said Carlson was fired for his criticism of Fox News' senior management.