A tentative deal is believed to have been reached in talks with senior US justice department officials.
The sale of overvalued mortgage-backed securities was blamed for the near-collapse of the banking system in 2007.
Last month, JP Morgan was fined almost $1 billion in a separate case over the “London Whale” trading debacle.
The scandal arose from disastrous trades by former bank employee Bruno Iksil, who made big bets on the financial markets.
The tentative deal to pay the $13 billion fine to the justice department was reached during the talks on Friday, between JP Morgan lawyers with US Attorney General Eric Holder and his deputy Tony West, the Wall Street Journal said, citing officials familiar with the decision.
The New York Times also reported that the investment bank was nearing the agreement, although final details are still being discussed.
Neither the justice department nor the bank was available for comment.
If confirmed, it would be the biggest settlement of its kind ever paid by an American company.
The $13 billion sum is said to include $9 billion in fines and a further $4 billion in relief for struggling homeowners.
In the run-up to the financial crisis, sophisticated financial products known as mortgage-backed securities were created by many investment banks.
What JP Morgan is alleged to have done was sell the mortgage-backed assets knowing full well that many of the home loans were in fact very risky.
The mortgage-backed assets are widely thought to have played a central role in the near collapse of the banking system when banks realized in 2007 that many of their assets were worth a fraction of their official book value.
The fine would settle all potential civil action that might be taken against the bank in future but does not mean that criminal cases against individuals are ruled out.
JP Morgan had initially aimed to persuade US justice department officials to drop the criminal investigation but the attorney general ruled that out, reports said.
In August, US government officials filed two lawsuits against Bank of America relating to mortgage-backed securities. Bank of America denied civil fraud in failing to disclose risks and misleading investors.
JP Morgan has found itself overwhelmed by mounting legal troubles lately.
Once the darling of Washington and Wall Street, it reported a rare quarterly earnings loss last week, mostly due to legal costs totalling $9.2 billion.
The bank lost $380 million during the quarter, compared with a profit of $5.7 billion in the same period last year.
JP Morgan says it has set aside a fund of $23 billion to deal with mounting legal costs.
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