Speaking via Instagram, The Gypsy King urged his undefeated Ukrainian counterpart to agree to the deal that was previously in place before plans fell apart in March.
The WBC champion wants to fight Usyk - who holds the WBA, IBF, and WBO titles - at Wembley Stadium this summer.
"I'm sick of all this back and forward 'he said, she said'. Why don't we just do this? Why don't we fight this summer," Fury said in the video clip.
"Me and you, at Wembley Stadium for the percentage you've already agreed.
"And if you want the rematch so desperately, you can have one. I don't need rematches, I don't need nothing because I'm going to cut you down like cheese.
"So here's the offer. Let's do the fight at Wembley this summer, me and you."
Usyk is rumoured to also be in talks to fight Deontay Wilder and Daniel Dubois, something Fury also commented on in his own unique and unfiltered manner.
"Forget about fighting Deontay Wilder who I've knocked out twice, and forget about fighting Daniel Dubois who's not on our levels," Fury continued.
"You've already beat Joshua. The only fight left is between me and you for undisputed.
"I know you didn't fancy it the first time so let's see if we can rekindle it and have a good fight for the fans.
"Let's get it on! Make the right decision."
It was revealed earlier this week that talks between the two camps had resumed, although the latest update was that negotiations were currently at a stalemate.
In other news surrounding the Mancunian, UFC commentator and podcaster Joe Rogan recently went viral for claiming Fury "wouldn't stand a chance" against UFC heavyweight champion Jon Jones.
"You want to talk about who's the baddest man on the planet? If Jon Jones and Tyson Fury are locked into a room, I'm pushing all of my chips on Jones," Rogan stated in an episode of his Joe Rogan Experience podcast back in March.
"Tyson Fury is an amazing boxer. He doesn't have a chance in hell of making it out of that room. He would have to catch Jon immediately with one punch, and I just don't see that happening.
"The threat of the takedown looms so large; that shot will come so unexpectedly. When he gets his hands around you, you'll be so stunned."
Fury again wasn't shy to share his thoughts on the debate: "I heard Joe Rogan say something about me, and I've been off all the social medias and didn't reply to that little p****, little bald-headed midget,"
"I heard him say that Jon Jones could f*** me up if we were in the room together. I don't think so. Not a man born from a mother could f*** me up, in a room, on our own," Fury continued.
"Whatever happens in that room, I'd be walking out. Not a f***ing problem.
A video recently circulated of Fury training in MMA, which seems to have captured the attention of fight fans as well as Jones himself.
"Hey Tyson, it seems like Joe may have struck a nerve," Jones wrote on Twitter after learning of the comments.
"I'll admit there's no one touching you in that ring right now, but let's not let that confuse you with what would happen if you stepped foot in my cage.
"If you ever want to put some of those questions you got going on to rest, give Dana (White) a call. I'll help you out."
"Jon, you talk about being in a cage, I'm not a cage fighter, mate. I'm a boxer — the best boxer, actually," Fury responded.
"So if you want to come into a boxing ring and fight me, be my guest. Let me know.
"You don't have to call anybody else, you call me because it's a boxing fight and I'm the boss in this game."
