Fightnews.com reported that Parker and American Jarrell Miller turned down an opportunity to fight Usyk, according to his promoter, Alexander Krassyuk.
Usyk (16-0, 12 KO's), 31, is the current undisputed cruiserweight world champion, but wants to move up a weight class to take on the best in boxing.
Cruiserweight is the weight division below heavyweight.
Higgins took to Twitter to on Sunday to deny that they'd rejected a deal to fight the Ukrainian, tagging the reporter in the post.