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.
In an interview with 'Doing the Rounds', Hearn was asked if there was a fighter he regretted not signing, to which he replied: "I guess you could say Tyson Fury.
"I had a chance to sign him. I was in Monaco, I think I could have signed him.
"I didn't want to give him the fights that he wanted to take at the time, because I thought it was just too much money and the fights weren't good enough – and I probably should have done it, to be honest with you.
"I looked at him and I thought, 'You ain't ever going to come back anyway, look at the size of you', but he surprised everybody and how wrong I was.
"Fury is definitely up there, and there's a few others. A few American guys that I probably had the chance to sign as well."
Photo Getty Images caption: Tyson Fury celebrates