CNBC's Maria Bartiromo reported earlier in the day that there would be no announcement Friday and that discussing Parsons' future with the company would not be unusual for the board at its recent meeting in London.
A Time Warner spokesman called the report a "rumor" and said no announcement has been made.
Time Warner declined further comment.
Parsons, whose contract ends in May 2008, took over the company in 2002 after a difficult merger with America Online and has been credited with improving the company's operations across its portfolio of movies, cable television and cable services companies.
His departure ahead of the contract's expiration and speculation that Parsons will retain the chairman role, has been long rumored.
President and Chief Operating Officer Jeffrey Bewkes was identified close to two years ago as the leading candidate to take over as CEO upon Parsons's exit. Some investors said they believed tough decisions on spinning off or selling off divisions, including AOL, would more likely to be made by Bewkes.