State senator Amy Klobuchar then confirmed the information in a message on Twitter.
The officer, Derek Chauvin, was fired on May 26 and initially charged with third-degree murder and second-degree manslaughter.
The other three officers involved were also fired but had not been charged.
The Star Tribune reported that Minnesota Attorney General Keith Ellison would aggravate the charge against Chauvin and also accuse Thomas Lane, J. Kueng and Tou Thao of helping and inciting a second-degree murder.
The newspaper cited multiple sources of law enforcement familiar with the case that spoke under anonymity.
Video showing Floyd’s murder has sparked sometimes violent protests around the world against police brutality and discrimination.
Floyd’s family and demonstrators have repeatedly called for criminal charges against the four officers, as well as more serious charges for Chauvin, who held his knee against Floyd’s neck, despite his protests that he could not breathe, and stayed there even after the man stopped moving.