The Times in London reported Saturday that following a recent board meeting in London, Parsons' time with the communications group became numbered and his probable successor was named.
Parsons reportedly will hand over his post to his current and longtime second-in-command, Jeff Bewkes.
While Parsons has been credited with keeping Time Warner afloat during a troubled portion of the company's past, his future with the group has been questioned repeatedly.
One argument against Parsons' role in the media group has been that he does not fit in the company's current corporate structure due to his reported sentimentality.
The newspaper said Bewkes is seen by some as being less sentimental overall and therefore better equipped to deal with possible changes in the company's struggling assets and business dealings in the future.