A high-profile clash between Paul and Fury has been discussed, with a December date mooted.
But 'The Problem Child' insists Fury doesn't cut it as his opponent while aiming a dig at pound-for-pound king Canelo and Floyd Mayweather's protégé Davis.
The 4-0 boxer continued by slamming the opponents of Canelo and Davis during their rise to stardom.
He tweeted: "7-0 Fury doesn't cut it for my 5th fight I'm fighting either Hector Lopez or Javier Martinez next!!
"Hector was 'Tanks' 8th opponent, came in 0-0 and retired 0-1. Hector was an MMAer who was 2-0 Javier was Canelos 10th opponent, entered the fight 0-0 and retired at 0-1 #Clowns."
7-0 Fury doesn't cut it for my 5th fight- Jake Paul (@jakepaul) October 24, 2021
I'm fighting either Hector Lopez or Javier Martinez next!!
Hector was "Tanks" 8th opponent, came in 0-0 and retired 0-1. Hector was an MMAer who was 2-0
Javier was Canelos 10th opponent, entered the fight 0-0 and retired at 0-1#Clowns
Paul improved his professional record against Tyron Woodley, outpointing the former UFC welterweight champion in their bout last August.
The YouTuber-turned-boxer remains the talk of the combat sport world, with Jorge Masvidal open to fighting him once his career in the UFC is over.
He said: "Right now, where I'm at in my career, I'm going to fight the world's best fighters. Right? We can both agree that in the f**king UFC and at 170 pounds, there's a lot of good guys that I can f**king beat up.
"And I'm going to get the most money for it, my brother.
"And when I am done beating up world-class fighters, this bum will still be around - I'll go and collect a quick paycheck for hitting him so f**king hard in front of the whole world.
"Those type of options will always be there. But right now, when I'm in my prime, I've got to do things that people in their primes do - and that's fight the world's best.
"He's not in that conversation."
Featured Image Credit: PA/Jake Paul