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.
"As Joseph Parker’s promoter, I confirm I have never received any communication from the Usyk camp regarding a fight, so your story is false."
Joseph Parker re-tweeted the message.
Krassyuk added there is a 70 percent chance that Usyk will make his highly anticipated move up to the heavyweight division and face either Alexander Povetkin or Luis Ortiz.
Despite only contesting 16 bouts, Usky has a big resume that includes an Olympic gold medal, and was recently named Fighter of the Year by Sports Illustrated and ESPN.
He also took Evander Holyfield's record for becoming the quickest cruiserweight to win a title in just 10 fights. Holyfield took 12 bouts.
Parker fought three times in 2018, losing to British pair Anthony Joshua and Dillian Whyte, but he ended the year in style with a knockout win over Alexander Flores.
Higgins told Sky Sports earlier this month that they'd consider returning to Britain for his next fight.
Australian Lucas Browne has also been discussed as a possible option.