The Kiwi heavyweight's clash with the rugged Chisora is "very much in play" for April 20 at the O2 Arena in the British capital, according to British promoter Eddie Hearn.
Originally it was suggested as an undercard fight for a night to be headlined by Dillian Whyte, the last fighter to beat Parker who subsequently knocked out Chisora.
But Whyte has been ordered to fight American Dominic Breazeale for the WBC's interim title, a fight that would put the winner in the prime position to the the mandatory challenger for the winner of the Deontay Wilder v Tyson Fury rematch.
Hearn doesn't believe the Whyte v Breazeale deal will be done in time for April 20 and is looking at alternatives, admitting promoting Parker is an option.
He also raised the prospect of trying to get British welterweight Amir Khan's world title fight with American pound-for-pound star Terrence Crawford as a double act.
"The April 20 show in London is definitely happening but I doubt it will be Dillian Whyte on that card," Hearn told IFL TV on Thursday (NZT).
Asked how progress was going on Parker v Chisora and if that could be an alternative, Hearn replied: "That is in play, very much in play. It could headline the O2, it could still be a monster card but it's not big enough as it's own event to be a pay-per-view.
"So do you add Khan on to that, do we marry up the two and do a big show through the night, do you add a bigger fight on the card? There are a lot of things that are in conversation."
Chisora against Parker is marketable. Chisora is a local legend and Parker has made his name in the UK with three of his last four fights coming there, including his world title loss to Anthony Joshua and a thrilling battle with Whyte that saw both fighters on the canvas before the final bell rang on 12 thrilling rounds.
Beating the respected Chisora would put Parker back into the title talk but it's a risky fight with a loss causing major damage to his current rebuild.
The quality of the opponent also means Parker's handlers at Duco Boxing need to get the deal done with Hearn as quickly as possible. Parker would want a full training camp in Las Vegas with coach Kevin Barry, mindful of being caught short against Whyte on the back of a rushed and truncated camp.
It's interesting times in a heated division and Hearn sees the latest development as positive for Whyte, saying if he can get past Breazeale he will be in a prime position to challenge for the WBC belt, currently held by the unbeaten Wilder.
But he expects the Breazeale negotiations to be difficult in terms of money and location and says he wouldn't be surprised if the fight went to purse bid. That would likely mean a July date for Whyte.
These developments came on a day when Hearn's main fighter, WBA, WBO and IBF champion Joshua, was confirmed for his first overseas title defence, with a June 1 date against American Jarrell Miller in New York