Another leading South Korean newspaper, the JoongAng Ilbo, carried a similar report.
However, South Korean authorities denied the reports, saying that Lee and the North Korean delegation had general discussions on improving relations but nothing related to a summit was mentioned.
The four-man North Korean delegation – led by senior ruling Workers' Party official Kim Ki-nam - visited Seoul from Friday until Sunday, to attend the funeral of former South Korean president Kim Dae-jung.
The former leader's so-called "Sunshine Policy" of engagement with the North led to the first inter-Korean summit in July 2000.
Cross-border tensions have risen sharply in recent months after the North made a series of threatening gestures, test-fired a barrage of missiles and conducted a second nuclear test which resulted in a tightening of UN sanctions.
Despite denials of a possible summit, Lee told the North Korean delegation during their meeting that he was ready to help the country rebuild its economy and asked that his intentions be relayed to Kim Jong-il.
He also reportedly told the delegation that the South does not want North Korea to collapse.
Ahead of the meeting North Korea has shown signs of softening its stance toward the South, freeing a South Korean worker held for more than four months, agreeing to lift restrictions on border crossings, pledging to resume suspended joint projects and the reunion of families separated since the Korean War.
Monday's reports of a possible summit meeting came as a US official in charge of enforcing UN sanctions on North Korea held talks in Seoul.
|Philip Goldberg, left, is in charge with enforcing UN sanctions against North Korea [AFP]
Philip Goldberg is on a regional tour seeking to maintain pressure on North Korea to return to six-party nuclear disarmament talks.
The UN sanctions are designed to ban business with North Koreans suspected of being in the illegal arms trade and with North Korean firms trading arms or other illicit materials.
Speaking alongside South Korean nuclear negotiator Wi Sung-lac, Goldberg said the complete denuclearisation of North Korea remained the ultimate goal.
He also urged the North to return to six-nation nuclear disarmament talks which it abandoned in April.
North Korea has said it considers as dead often-stalled disarmament-for-aid talks that bring together envoys from the two Koreas, China, Japan, Russia and the US.
It has signalled that it instead wants only direct dealings with the US, something Washington said it would not do.