David O. Russell -- the Oscar-nominated director behind "The Fighter" -- is under investigation in Florida for copping a feel of his 19-year-old transgender niece ... but Russell told cops it was totally consensual.

The Broward County Sheriff's Dept. has confirmed ... Russell has been accused of inappropriately grabbing his niece's breasts during a workout session at a South Florida hotel gym on Dec. 30.

According to the police report taken 3 days after the incident, Russell's niece ... who was born a man and is currently in the preoperative phase of her transition ... told cops the two had been doing abdominal exercises when he asked questions about her transformation.

The niece -- who does NOT have a blood relation to Russell -- told cops they began to talk about her breasts ... and how certain hormones she's taking have made them larger.

According to the report, the niece claims Russell then "put his hands under [her] top and felt both breasts."

Cops say the woman said she felt "uncomfortable" ... but admitted she "did not ask him to stop at any time."

Investigators later contacted Russell ... and according to the report, the director confirmed he DID touch his niece's breasts ... but only after she gave him permission.

Cops say Russell explained that during the conversation about her chest, the niece informed him that one of her breasts was bigger than the other. The official report says ... Russell told cops his niece then "allowed [him] to feel both of [her] breasts."

According to the report, Russell told cops his niece asked him to "pinky swear" that he would never tell anyone about the incident.

In the report, cops say Russell insisted he repeatedly asked his niece if she was ever uncomfortable during the incident ... and claims she gave consent.

In the police report, one of the investigators notes, "Russell stated [his niece] is always causing drama since the transgender transformation and has become very provocative and seductive."

TMZ spoke to a source extremely close to the family who said the niece only filed the report because she felt "violated by someone who was very close to her" ... and she wants to make it clear that even powerful people should be "held accountable for their actions."

Cops tell TMZ ... the case is currently under investigation and authorities plan to re-interview both parties. The case will eventually be submitted to the Florida State's Attorney's Office, which will decide if criminal battery charges will be filed.