The British fighter has been indicating that he could return to the ring in recent days and his promoter hopes that this is the case so that he can finally take on rival Anthony Joshua in a much-discussed bout.
Speaking to ESPN, Warren said: "I've seen it [Fury's social media video hinting at a comeback] yesterday, I haven't spoken to him. He's always got a twinkle in his eye.
"I will not ever say to him or ask him to come back and fight. If he chooses to do that, that will be his choice.
"He has to go in the gym, he does that for peace of mind. I know it's very important to him and it's good he's in the gym.
"I would like to see it [the fight against Joshua] just to clean up the ... well lack of controversy because it never happened. I would like to see the fight happen but it's up to the guys. If they want to do it, get it on."
Fury, who announced his retirement from the sport in January, gave another strong hint that he could return as he responded on social media to an interview given by heavyweight world champion Oleksandr Usyk - who defeated The Gypsy King twice last year.
Asked about Fury's apparent retirement, the Ukrainian fighter said: "He's not retired. I think Tyson will continue training, continue boxing, because he's a great man.
"Yes, Tyson Fury... a lot of speak - blah blah blah blah - but it's good. Great man, wow."
Reacting to Usyk's words, Fury commented on Instagram: "Beat the f***** 2 times the world knows the truth.
"Any time, any place. sucher (sic) UK next time 100k people."