Tommy, 22, notched up his sixth professional career win on Saturday with a victory over Jordan Grant after four rounds.
However, the former Love Island star has been involved in a heated war of words with YouTuber Paul in recent months.
Tommy has been vocal about his desire to step into the squared circle with Paul, saying he "would take the complete p**s out of the man" in a fight.
Meanwhile, Paul entered the world of boxing in 2020 and holds a 3-0 record after wins over AnEsonGib, Nate Robinson and Ben Askren.
The 24-year-old American has traded verbal blows with Tommy and even involved the boxer's partner, Molly-Mae Hague, in one of their spats last month.
Big John admitted that he respected Paul for "doing what he's doing," but he made it clear that he wants to set up a fight with Tommy.
The 57-year-old went on to issue a challenge to the YouTuber-turned-boxer for him to step into the squared circle on the Fury vs Wilder undercard.
"Good on Jake Paul for doing what he's doing," John told BT Sport.
"At the end of the day, good luck to the geezer. Anyone who gets in the ring is a game man."
Speaking to Steve Bunce on BT Sport, Big John added: "Jake Paul, we'll have you next mate.
"If you think he's good, then we will take Jake Paul next. Tyson's undercard, July 24, Jake Paul."
Paul is set to return to action on 28th August against former UFC welterweight champ Tyron Woodley.
Tyson, meanwhile, is slated to make the first defence of his WBC title on 24th July against former champ Wilder in Las Vegas.
However, the proposed plans for the all-British showdown fell through after Wilder won his arbitration case and a trilogy fight with Tyson was confirmed.
Featured Image Credit: PA/BT Sport/Instagram
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