It was first announced in September that the cable channel was planning a new version of the drama series, which originally ran on CBS from 1978 to 1991.
Wright told Variety: "I don't want to give away the plot, but [writer Cynthia Cidre] found something authentic to business and to Dallas that allows them to trade on the same dynamic of the super wealthy."
He went on to say that the new series will continue to focus on the "upstairs, downstairs paradigm" of the original show.
"If it wasn't the rich and poor [creating a conflict], it was attitude," he explained. "Entitlement versus a populist point of view. This [new show] covers all that."
Wright also revealed that TNT is still hoping to reach a deal with original star Larry Hagman to make an appearance in the revived series.
Hagman previously suggested that negotiations had come to a "crashing halt" and that he "didn't know" the current status of the project.