The bank is negotiating a settlement with U.S. Attorney Preet Bharara's office over the matter that will likely include a fine and a deferred prosecution agreement, the Journal reported.
A spokesman for the bank could not immediately be reached for comment on the Journal story.
JPMorgan had raised concerns with UK regulators about Madoff more than a month before his arrest in December 2008, the Journal reported. In a document filed with Britain' Serious Organized Crime Agency, the bank raised several concerns about Bernard L Madoff Investment Securities, such as returns that appeared "too good to be true," the Journal said.
Madoff had a banking relationship with JPMorgan for two decades, the Journal said.
In addition to the Madoff case, prosecutors and the Federal Bureau of Investigation are examining whether there was a larger pattern of failed controls at the bank, the paper said, citing people close to the probe.
Madoff is serving a 150-year prison sentence after pleading guilty to running a Ponzi scheme that cost investors billions of dollars.
JPMorgan has said it did not know about the fraud, the Journal said.
Suspicious activity reports are required when a bank finds suspicious transactions or signs of a violation of federal law.
The Madoff probe comes as JPMorgan grapples with a string of legal troubles. Over the past few months, it has agreed to pay nearly $20 billion to settle lawsuits and probes, the Journal said.
(Reporting by Dena Aubin; Editing by Eric Beech)