Sheen was furious after Blair complained to the sitcom's executives that her co-star was frequently late and unprofessional on the show's set, the celebrity news website said.
Sheen then said he fired the actress and will not work if she returns to the production.
The actor also wants series bosses to offer actress Mila Kunis a 10-episode story arc for $1 million per episode, TMZ said.
Kunis is the girlfriend of Ashton Kutcher, the actor who replaced Sheen after he was famously fired from his hit series "Two and a Half Men" after eight seasons because of his drug use, insubordination and erratic behavior. Sheen began starring in the new show "Anger Management" last year.