Cox plays Lucy Spiller, a tabloid queen. Aniston will appear in the season finale as Tina Harrod, a rival magazine editor and a lesbian, according to the report.
An FX Networks representative declined to comment.
The episode will air March 27. It will be the first time the two "Friends" co-stars have worked together since the sitcom went off the air in 2004.
"Dirt" explores the relationship between the tabloid industry and the entertainment business, using Cox's ruthless character as the focal point.
FX Networks is owned by News Corp., the parent company to FOX News.