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.
"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.
"Painfully earned justice has finally arrived for George Floyd's family," tweeted Crump, the Floyd family lawyer, as Derek Chauvin was found guilty in a unanimous decision by a Minneapolis jury.
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.
"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.