The 33-year-old fighter is expected to get into the ring in September after being named as the next mandatory challenger for the victor of Oleksandr Usyk vs Daniel Dubois, which is set to take place on Wembley on 19 July.
However, Parker has now been given approval from the WBO to set up a trilogy clash with 41-year-old Chisora, who is currently ranked No. seven.
When asked whether a third Chisora fight was on the cards, WBO president Gustavo Olivieri told Sky Sports: “Yes, Parker may defend his interim title against any of the top-15 WBO world-rated contenders.”
Parker’s promoter David Higgins revealed the boxer was open to setting up a third fight with Chisora.
He said: “I'm sure he would be [open to a third fight], yes.”
A Queensbury spokesperson then said the organisation was “working on our autumn events schedule and looks forward to announcing some great events in due course” when asked about a possible third Parker vs Chisora match.
In their first bout, Parker beat Chisora by a split decision in May 2021, with the New Zealander beating his opponent on points again in their rematch seven months later.
Following his second fight with Chisora, Parker said he was open to making their clash a trilogy.
Speaking to The Ring, he said: “I'd like to be out ASAP.
“I know Usyk and Dubois are fighting on July 19, I'd like to either fight not long after that, or it'd be great if I could be on the same card.
“That's been floated by Queensberry, so it'd be nice. Who do I fight? I'm not sure. The belts are held up at the moment.
“Usyk and Dubois have the belts, and whoever wins, who knows what kind of rematch clauses are in the contract.
“It'd be nice to fight anyone. It'd be nice to fight someone like Derek Chisora. He is looking for his 50th fight, and I'm not sure if he's going to fight for a title.
“I know I've beaten him twice, but I've never had a trilogy in my career, so Derek always brings it, and it could be a good sort of fight to keep me busy.”