Paul, 24, last beat ex-UFC fighter Ben Askren in the ring but is already setting his sights far higher when it comes to taking on the best boxing has to offer.
Speaking to TMZ, Paul said: ‘I just want to continue to be the most disruptive boxer in the history of the sport.
‘I think it’s about taking it on a fight by fight basis and continuing to build these fights and making them even bigger, taking on more serious opponents.
‘If you asked me if I was going to be where I’m at [now] three years ago, I wouldn’t believe you. So I don’t want to [put a] cap on my possibilities, I’m open minded and I think anything is possible.
‘I think I could be fighting Canelo Alvarez for the WBC or WBO championship belt.’
Whether Canelo will fall for Paul’s consistent call-outs is up for dispute.
The Mexican has shown a distaste for any fight cards with the Paul brothers on and reacted on social media with a face-palm emoji when Logan Paul boxed iconic – but retired – fighter Floyd Mayweather in an exhibition bout.
Canelo is the pound-for-pound king of the sport and any serious victory over him would be one of the great upsets in all of sport.
But Paul is not lacking in confidence and believes he is on a path that can take him to superstardom at the top of the sport.
‘The sky’s the limit and it’s just about how serious I’m going to take it and I do take it seriously – more seriously than 99.9 per cent of these ‘professional’ boxers that are out there,’ he added.
Before he can start dreaming of world title belts Paul needs to face-off with Woodley in the ring as the ex-UFC star prepares for his boxing debut.
Paul believes Woodley is set for the same fate as his previous three opponents – all beaten by knockout – and believes he can drown him with his ‘overwhelming’ qualities in the ring.
‘My pro fights haven’t lasted long, but in sparring, I love taking my opponents into deep waters and drowning them with my overwhelming cardio, consistency, and precise punch selection… Soon we will see how well Tyron can swim,’ Paul wrote on Instagram.
However, former UFC welterweight champion Woodley has backed himself to knock Paul out inside three rounds when he makes his professional boxing debut on 28 August.
Asked what round Paul will go down in, Woodley told the ‘Believe You Me’ podcast: ‘I think three.
‘First round sounds cocky, sounds dope, but I just know that if I’m fighting Tyron Woodley, everyone is going to tell him to cover up, weather the storm, clinch him, grab him, keep him away from you, stay at distance, watch out for the right hand.
‘I’ve got to set a couple of traps so I may need a round or two to set some traps, see what he responds to and I think third round I should be able to clean up the deal.’