"Korea Development Bank has considered M&A deals in foreign investment banks including Lehman Brothers, and asset management companies, as part of its privatisation and competitiveness efforts but nothing has been decided yet," it said in a statement.
A report in the Chosun Ilbo newspaper said KDB had proposed taking a 25 percent stake in Lehman in a deal worth up to 6 trillion won ($5.3 billion) and involving other Korean banks.
It quoted an unnamed financial industry source.
Yet two banks cited in the report distanced themselves from the idea.
"We have not seriously considered the idea and have no plans to do so in the future," said a spokesman at Shinhan Financial, South Korea's second largest.
Third-ranked Woori Finance said: "We have not received any offer about the Lehman deal nor have we considered it internally." The smaller Hana Financial reiterated a previous denial.
Europe's biggest bank, HSBC, is also interested in Lehman, according to the newspaper report.
But HSBC is unlikely to make a move for Lehman, people familiar with the matter said.
Speculation it could be interested has circulated for several weeks, but the bank has reduced its investment banking appetite and executives say investment will be in emerging markets.
HSBC declined comment.
KDB needs other banks to come aboard after Korea's Financial Services Commission this week expressed concern at the idea of a state-led bank leading any investment in Lehman.
Lehman prefers KDB, whose CEO used to head the U.S. bank's South Korean operations, over other contenders as KDB plans to keep its management after a deal, the paper said.
It might get backing from South Korea's military savings fund, whose chairman told Reuters it would consider joining KDB in any bid for Lehman.
Lehman is under pressure to raise capital as Wall Street firms reel from the fallout of the subprime mortgage crisis and is looking for buyers for some $40 billion in commercial mortgages and property on its balance sheet.
It received more bad news on Tuesday when hedge fund manager Ospraie Management, in which Lehman owns a 20 percent stake, said it would close its flagship fund after it plunged 27 percent in August on losses in energy, mining and natural resources equity holdings, in one of the biggest ever closures of a commodities-focused hedge fund.
Lehman shares were up 1 percent in midday trading.
Shinhan shares fell 2.6 percent while Woori shares rose 0.8 percent, both lagging a Korean share index which ended up 1.4 percent.
HSBC shares in London were down 1.3 percent at 876 pence, in line with a weak UK share market.