Tyson Fury and David Haye, whom Parker was due to meet in a mandatory challenge to his WBO title before the Englishman decided to take what many regard as an easier fight against cruiserweight Tony Bellow, sent Parker messages after his victory, saying "there were big things ahead".
Earlier this year Fury had praise for the New Zealander.
"I like what I see with Joseph," Fury told Sky Sports UK.
"He's a really nice guy, I speak to him a lot on the internet, on Twitter, give him advice and that, and he takes it on board," he said ahead of Parker's victory over Carlos Takam in May.
"He will have to get another couple of fights, 10-rounders in, and good fights, while he waits for his opportunity to fight as mandated challenger, but he can fight, and he's tough and ambitious.
"I like him, he's my type of fighter, Joseph, and I wish him well."
Parker is tipped to fight Hughie Fury, the cousin of Tyson, next year to his first defence of the WBO title.
