The US based firm has offered an additional 50 cents on top of its prior offer which was rejected by TWE back in April. The current offer of $5.20 per share is 5.1 percent above TWE’s Friday closing price of $4.95 per share, ABC News reports.
In a statement issued to the company’s shareholders, TWE say that they are willing to “engage further” with KKR on the proposal.
"The board of TWE, together with its advisers, has concluded, based on the revised proposal, that it is in the interests of its shareholders to engage further with KKR and Rhone," the statement read.
In addition to a possible sale, TWE is continuing to rebuild the health of its balance sheet following last financial year’s write-off of close to 600,000 cases of wine.
Last month, TWE announced its expansion into the $US39 billion global travel retail market by securing shelf space at some of the world’s top airports, cruise liners and duty free shops.
According to TWE, the wine category has remained relatively undeveloped at airports with spirits dominating alcohol sales at 70 percent. The global wine company believes that its flagship brands, Penfolds and Wolf Blass, will be able to tap into the high-spending travel market, particularly with travels from China.