Hana Financial Group chairman Kim Seung-Yu and Lone Star Funds chairman John Grayken met in Tokyo on Wednesday and decided to extend the May 24 deadline, the Korea Times reported.
The two sides will continue to discuss the terms of the deal over the weekend before making an announcement, it said.
"The two agreed not to greatly alter the content of their current contract," a source was quoted as saying.
Hana, the country's fourth largest banking group, declined to confirm the report. But a spokesman said both sides have been in contact in an attempt to extend the deadline.
Lone Star struck a deal with Hana last November to sell its 51 percent stake worth 4.69 trillion won ($4.32 billion). But the deal is is doubt because of an ongoing court case.
The regulatory Financial Services Commission said last week it probably would not rule on the deal by a May 24 deadline. Either side can abandon the agreement unless the transaction is completed by then.
The regulator said it would delay its decision because of the court case, which could negate Lone Star's legal status as KEB's largest shareholder.
Under South Korean law, if Lone Star is to be eligible for the status, it must have been free of legal violations for the past five years.
The Supreme Court in March overturned the acquittal of the US fund's former head of Korean operations for stock price manipulation. It ordered that the case be heard again.
Choi Young-Il, an analyst at Moody's Investors Service, said in a report Monday that the delay could hurt the credit ratings of both companies due to increased uncertainty.
"Hana Financial would eventually need to deploy its surplus capital either by seeking alternative acquisitions or buying back its shares, given the pressure from unhappy shareholders," he said.