The former WBO heavyweight champion has targeted the top-ranked WBO heavyweight according to his manager David Higgins.
Parker is coming off an impressive win over Derek Chisora late last year.
"He fought Chisora and dominated him so his brand equity in the world and United Kingdom is at an all-time high," Higgins told Sky Sports.
"The question is 'who next?' Joseph has signalled that he'd like to fight as soon as humanly possible. A possible opponent is Joe Joyce.
