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.

"At this point in time," Chiodo said, "we have not been contacted by anyone for police assistance or that would like to file a police report."

"When anyone does contact us we will be responsive, we are only a phone call away for any citizen or visitor to Inver Grove Heights or they can come in person to our police station to file a report or ask for any police assistance."

As we previously reported, Trimble -- in her lawsuit -- claims Cook punched, hit and threw her violently during an altercation in Inver Grove Heights, Minn. in Nov. 2020. She says she was left a bloody and bruised mess.

She claimed at one point during the incident, Cook held a gun to her head and told her she was going to die. She also said the Minnesota Vikings player held her against her will for hours -- before eventually letting her go.

In her suit, Trimble never said she went to cops over it all, but we've reached out to her attorney to see if she now has plans to -- but so far, no word back.

As for Cook, he's maintained he was the real victim, saying Trimble broke into his home and held him hostage at gunpoint. Dalvin's reps claim the accusations are nothing more than an attempt to extort the football player.

It's worth noting, police also tell us they are NOT investigating Trimble, either.

"I just want everybody to know I'm the victim in the situation," Cook told reporters earlier this week. "The truth and the details about the situation will come out at a further time."