The number, which reportedly includes many westerners including perhaps 250 Americans, represents a doubling of last year's US assessment and will dismay US war planners.
The New York Times' report cites anonymous "intelligence and law enforcement officials."
In recent weeks, there have been allegations that the US military has been playing down the IS threat in intelligence reports, to paint a rosier picture of its efforts.
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But US President Barack Obama will on Tuesday next week chair an international summit on the sidelines of the UN General Assembly for leaders fighting the IS group and "violent extremism."
And on Tuesday, a US Congressional report into foreign fighter flows is expected to paint a bleaker picture, suggesting that a year of US-led air strikes has not slowed recruitment.
Aside from the aerial bombardment of IS targets by a US-led coalition of Arab and Western powers, the Pentagon has also set up a $500 million program to train "moderate" Syrian rebels.
But this, too, has proved an embarrassment.
A first cross-border foray by 54 US-trained fighters was defeated by an Al-Qaeda linked militia and a second appears to have traded many of their arms to jihadists for safe passage.