The fugitive exchanged shots with federal officers in California’s Big Bear Lake region, according to the Los Angeles Times.
Two officers are reported to have been wounded and one airlifted to hospital.
Christopher Dorner, 33, has been on the run since last week, after the murders in southern California.
He had sworn revenge on police officers he blamed for his sacking in 2008.
US television networks showed police and vehicles surrounding a cabin, but it was not clear if Christopher Dorner was inside.
Authorities near Big Bear Lake in the San Bernadino mountains were alerted after Christopher Dorner reportedly broke into a house and tied up two people.
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