The New Zealand boxer is set for a bout with Junior Fa later this month but is considering a clash with Chisora, according to his manager David Higgins.
Higgins said of the British fighter: "One hundred per cent he's a serious option.
"Obviously Joseph's own focus is Junior Fa and that's the way it should be but my job is to look ahead.
"In yachting terms, I'm the guy on top of the mast looking for the next shift."
Higgins revealed that Parker would be happy to fight his rival in London as Chisora has demanded.
He said: "Joseph will fight anyone anywhere and if has to go to London to fight Chisora he will."
The pair had been set to fight in 2019 but Parker pulled out with an illness caused by a spider bite, although Chisora felt his opponent was just frightened of him.
He said: "I signed the fight, flew to his camp in LA to film, only for him to chicken out and claim a spider bite was the reason he couldn't step in the ring with me.
"The truth is, when he sat across the table, looking in my eyes, reality hit, he wasn't ready for the war I bring."
Higgins added that a fight between Parker and Chisora "makes sense" as all parties are interested.
He told Sky Sports: "We'd endorse it and there is interest from Parker, and our management team would endorse it.
"There was a lot of talk in the past. The fight was contracted at one point. I think that fight makes sense."