Online news outlet MoneyToday cited an unnamed industry source as saying that KKR had revised upwards its bid price for the beer maker to more than $1.9 billion and accepted most of InBev's demands.
An OB official confirmed that KKR had been picked as a buyer, declining to be named because he was not authorized to speak to media.
OB could not immediately reached for comment.
The report said the U.S.-based private equity house got a high score in the financing plan with strong commitment from foreign banks, than two other bidders -- Affinity Equity Partners and MBK Partners.
Three private equity houses -- Affinity Equity Partners, Kohlberg Kravis and MBK Partners -- have made final offers for South Korea's OB, the official of the beer maker had said last week.
Anheuser-Busch InBev, the world's largest brewer and the owner of OB, accepted the offers this month, which it has valued at more than $2 billion, as part of an effort to sell non-core assets and to repay debt.
(Reporting by Kim Yeon-hee; Editing by Chris Lewis)