South Korean marines guarding the Han river, which flows into an estuary and meets the North's Imjin river, found the man lying on the river bank, apparently suffering from exhaustion, the South's Yonhap news agency said, citing a South Korean government official.
The man, who is believed to be in his late 20s or early 30s, told South Korean authorities he wanted to get to North Korea to meet its leader, Kim Jong Un, Yonhap said.
The two Koreas are technically at war after their 1950-53 conflict ended in a truce and not a peace treaty. Their border is one of the most heavily militarised in the world and unauthorised bids to cross it can spark clashes.
South Korea's defence ministry could not immediately confirm details of the report but an official said an American man was picked up by the military late on Tuesday and was being questioned.
The incident comes after a young American man, Matthew Miller, was detained in the North after entering as a tourist in April. He was sentenced to six years of hard labour on Sunday for committing "hostile acts" towards the North Korean state.
There have been no cases of Americans entering North Korea from the South without legal authorisation in recent years.
A South Korean man was shot and killed by South Korean soldiers in September as he was apparently trying to enter the North by floating across a border river.
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