The two rivals have been scheduled to fight on two occasions in the past after trading insults and Warren is hoping to close a deal for a bout in early 2023.
The promoter told talkSPORT: "It will probably be in late February or March. The reason why it didn’t go [before], the contracts were all signed, because of the problems he had with the US immigration. We are all past that now. Jake is up for coming over here and we have to get the deal finalised in the next week or so."
The fight was originally slated for last December before Fury withdrew due to injury. It was rescheduled for August but was called off as the 'Love Island' star was unable to enter the US due to visa issues.
If the bout is made, Warren is expecting Fury to come out on top.
He said: "I’ve got to fancy the boxer, Tommy, to beat him. That’s why I’m keen on making it. It’s life-changing money for Tommy and it’s a no-brainer for him to fight him.
"Jake Paul is obviously taking it very seriously now. He’s got a license and he is training very hard. What level he is at you are only going to find out when he fights a Tommy Fury."
Fury defeated Rolly Lambert in an exhibition bout in Dubai recently but Paul was ringside to provide scathing commentary on his rival.
The YouTuber said: "This can’t be real, right? Like, is he actually trying? Or are people gonna actually pay me to fight this guy?"