Matchroom promoter Hearn said he had tentative discussions with Fury about joining his stable when the pair were both in Monaco in 2017 but a deal was not agreed.
Fury had battled problems with recreational drugs and depression in the two years since dethroning WBA, WBO and IBF heavyweight champion Wladimir Klitschko, while he ballooned to 27 stone in weight.
Earlier this year, Fury completed a remarkable turnaround to defeat Deontay Wilder and become the WBC heavyweight champion.
