Lone Star paid $1.2 billion for the venture back in 2003. Today, it's worth approximately $3.4 billion.
Lone Star will be able to sell as soon as the contractual ownership period expires at the end of October.
Officials at Lone Star said that the firm hasn't outlined any sale plans quite yet, and it has not finalized its decision on selecting an advisor to assist with the plans.
The U.K.-based banker HSBC, which has unsuccessfully sought a stake in a South Korea bank three times, is an early suitor, the report said.