Dez Bryant -- Cops Aware of 'Alleged Illegal Possession' Of Monkey

The Dez Bryant pet monkey saga has reached new heights -- with Dez's personal attorney reaching out to cops in an effort to avoid a criminal investigation.

As we previously reported, animal rights groups went bananas after Dez posted a pic with a domesticated Capuchin monkey which he named Dallas Bryant ... a monkey that appeared to be his new pet.

Now, officials in DeSoto, TX -- where Dez is believed to reside -- tell TMZ Sports they have been made aware of the "alleged illegal possession" of the monkey within city limits.

In fact, the DeSoto PD has issued a statement saying, "The City Attorney was just contacted by Mr. Bryants’ personal attorney who advised the monkey is NOT in the City of DeSoto."

"The DeSoto Police Department is in contact with the City Attorney, the Dallas Cowboys organization, and Mr. Bryants’ personal attorney, regarding this matter. We have also been in contact with PETA and the North America Primate Sanctuary Alliance in an effort to address their concerns."

"It should be noted, that as of this date, the DeSoto Police Department has no evidence that the Capuchin monkey is in the City Of DeSoto."