Hearn has become increasingly optimistic as this week has gone on that he can bring the two fighters together in a contest for Joshua's IBF world heavyweight title.
Speaking in Glasgow ahead of Ricky Burns' WBA world super-lightweight title clash with mandatory challenger Kiryl Relikh, he appeared confident of striking a deal.
Asked when an announcement on Joshua's next opponent can be expected, Hearn told Sky Sports: "Next week, for sure. We're getting close now.
