Talks are ongoing between the two financial institutions, although neither bank is willing to comment further on the matter.
Lehman is widely predicted by analysts to sell large stakes in itself, after being hammered by credit losses and asset writedowns due to the global lending freeze.
Shares in the US firm are trading at around 75 per cent below last year's peak.
It has taken a $8.2 billion hit on mortgage-related assets over the past 12 months.
Speaking to Reuters, an unnamed Korean bank executive expressed scepticism as to whether KDB could pull off the agreement.
"We need to wait until a deal is done," he commented.
"It would be in the form of buying new shares or existing shares. But this kind of deal still has a high possibility of falling through, because Lehman could be in talks with other banks in other parts of the world."