NEW YORK (Reuters) - Transocean Ltd has disclosed that billionaire activist investor Carl Icahn has acquired a 1.56 percent stake in the offshore rig contractor and is looking to increase that holding.

Icahn is seeking regulatory approval to acquire shares worth more than $682.1 million, according to a statement on Transocean's Web site.

If he gets approval, Icahn would become one of Transocean's largest shareholders with just over 5 percent of the company, based on its closing stock price of $54.09 on January 11.

Transocean's biggest shareholder is Capital World Investors, a division The Capital Group Companies Inc, which owned 5.12 percent as of October 15, according to Thomson Reuters data.

Icahn's move comes less than two weeks after Transocean agreed to pay $1.4 billion to settle U.S. government charges over BP Plc's massive Gulf of Mexico oil spill in 2012 . Transocean employed nine of the 11 workers killed in the accident.

(Reporting By Jessica Toonkel; Editing by Paul Tait and Stephen Coates)