"I have no position in Time Warner. No options, no forwards, no stock," Icahn said when reached by phone.

Reuters and the New York Post reported on Monday, citing anonymous sources, that Icahn was building an equity stake in Time Warner.

Icahn waged an unsuccessful break-up campaign against Time Warner in 2006, when current Chief Executive Jeffrey Bewkes was the No. 2 executive at the company. In 2014, Time Warner snubbed a takeover offer from Twenty-First Century Fox Inc that valued it at $85 per share. Time Warner shares ended trading on Tuesday at $71.09, up 2.1 percent.