The WBC heavyweight champion announced his retirement from boxing after picking up a stunning knockout victory over Dillian Whyte at Wembley Stadium last April.
Fury is still in training, though it's unknown whether the unbeaten Brit will return to take on the winner of Oleksandr Usyk vs Anthony Joshua.
Warren told Sky Sports: "I speak to him all the time. If he wants to fight, he'll fight. I'm not going to tempt him. Because if he needs that then he shouldn't be fighting.
"It's got to come from him and his heart," he added. "Do I think we'll see Tyson in a ring [again]? I do because I think he's a fighting man and I think he'll miss it too much.
"The fans love him. He's got a real rapport with the man on the street. He's different class. And he'll do what he wants to do."
Joshua and Usyk will square off on August 20 as the Brit looks to win back the WBA, WBO and IBF heavyweight belts.
Warren believes Fury would be able to take out Usyk should the two meet inside the ring.
The promoter was also surprised by Joshua's strategy in his defeat against the Ukrainian.
He said: "I saw [Usyk] against Chazz Witherspoon, he had that fight and then he obviously fought [Derek] Chisora and he looked alright. Against Joshua he looked different class.
"[Joshua] didn't use any of his physical attributes. I didn't understand why.
"I felt that he would out-jab him or keep him on the end of the jab and let the right hand go but he didn't. He was getting out-jabbed by a smaller guy on the outside.
"I thought the only way Usyk was going to do any damage was to get underneath inside and work inside. But he didn't have to do that. He was beating him on the outside.
"How do you fight him? I really do fancy Tyson to beat him. I think Tyson is a similar guy in some ways and a much, much bigger guy."