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Dalvin Cook Not Under Police Investigation ... Cops Say Alleged Victim Hasn't Filed Report

A police investigation into allegations that Dalvin Cook beat up his ex-girlfriend is NOT currently underway ... TMZ Sports has learned.

Despite domestic violence allegations against the NFL star in a new lawsuit filed by Cook's ex, Gracelyn Trimble, this week ... the Inver Grove Heights P.D. tells us it has not been contacted by any alleged Cook victims -- and therefore, has not launched a probe into the football player.

But, the Inver Grove Heights chief of police, Melissa Chiodo, said that all could change if someone does file a report.