Cormier, 41, has said this will be his last fight before retiring.
Miocic beat Cormier by fourth-round TKO on Aug. 17, 2019, to regain his belt after Cormier knocked out Miocic on July 7, 2018.
“I don’t have a location yet, but the trilogy with those two great heavyweights will happen this summer,” White said.
Miocic has been recovering from surgery on a torn retina he suffered in his last fight with Cormier. He said there were accidental eye pokes that caused the injury. Miocic also is a firefighter in a Cleveland suburb and has been putting in extra hours during the coronavirus pandemic.