By Mike Stone and Michael Flaherty

Jan 11 (Reuters) - Billionaire activist investor Carl Icahn is building an equity stake in Time Warner Inc, people familiar with the matter said on Monday, in a move that could lead to a major shake-up of the media conglomerate.

Icahn's intentions when it comes to Time Warner are not yet known, the people said, asking not to be named because the matter was private. Time Warner declined to comment.

Time Warner, the owner of cable channels HBO, TNT, TBS and Cartoon Network, said in November that ratings for its key domestic entertainment networks had dropped more than expected. Its shares have fallen around 30 percent since last July.

The New York Post said on Sunday that Icahn was believed to be buying up Time Warner shares and "will take another run at the company," citing anonymous sources.

(Reporting by Mike Stone and Michael Flaherty in New York; Editing by Richard Chang)