Floyd's daughter Gianna, his mother, sister and brothers will be among those attending private talks with Biden at the White House, Press Secretary Jen Psaki said.
The Floyd family has worked closely over the past year with other families, lawyer Ben Crump and civil rights leader Al Sharpton to push their anti-racism message.
Neighborhood theaters are set to start reopening on September 14, however, and the mayor of New York, Bill de Blasio, recently announced a major campaign to revive tourism from June.
"We need to work together to find a consensus. Let's get it done next month, by the first anniversary of George Floyd's death," Biden told US lawmakers during a joint session of Congress.
Chauvin, 45, could be handed decades behind bars for Floyd's May 25, 2020 killing, which sparked protests against racial injustice around the world and is being seen as a landmark test of police accountability.
Prosecutors have acknowledged that Floyd had fentanyl and meth in his system at the time of his death but introduced testimony from several medical experts who said the doses were not lethal.
But clashes broke out again soon after as another group of several hundred protesters gathered outside the Brooklyn Center Police Headquarters and were met with teargas and flash bangs.
"This was murder - it wasn't a lack of training," Arradondo said last year in a statement on the video footage of Chauvin, who is white, kneeling on the neck of Floyd, a 46-year-old handcuffed Black man, for more than nine minutes.
Chauvin has pleaded not guilty to murder and manslaughter charges, arguing that he did only what he was trained to do in his 19 years as a police officer.
He was held on a marijuana possession charge, though he had less than two ounces, which is a misdemeanor, Allen, Texas, Police Department said .
Scott died later that night after having been restrained and pepper-sprayed following his handover to the county jail, the New York Times reported, adding that a spit hood had been placed over his head.
"It's been nights I stayed up apologizing and apologizing to George Floyd for not doing more and not physically interacting and not saving his life," she said.
But Chauvin's attorney countered that he would prove that Floyd was on drugs, forcing officers to take tough action, and that his death was caused by the drugs and a medical condition rather than asphyxiation.
