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Speculation around the bout has been brewing for some time and details of the fight are currently being ironed out.
An agreement is close to completion and an announcement could be made in the next two weeks.
The fight would likely take place in March or April next year and Duco Events, the company that run Parker’s promotion, are looking at potential venues.
They’ve identified the Nou Camp, which has a capacity of more than 99,000, as a possible location, according to director David Higgins.
Zlatan Ibrahimovic and Anthony Joshua backstage in Cardiff
MARK ROBINSON
“A lot of English would go for a week in Spain. I'm throwing it out there as a possibility, without having any discussions with them.”
Duco Events director David Higgins
“The reason I threw Barcelona out there, is because I know the English love to go to Spain and there will be a lot of expats in Spain,” he told Sky Sports.
"It's a short flight. That stadium is massive. They're not in need of tourists, they probably think they have too many, but if it's off the main tourist season then as an economic thing, it would stack up.
"A lot of English would go for a week in Spain. I'm throwing it out there as a possibility, without having any discussions with them.
“Like I said, we have got a track record. The Jeff Horn-Manny Pacquiao fight delivered a massive economic return and was seen I think as a wise investment."
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Joshua and Parker are both unbeaten and take three a combined three belts into the fight.
Eddie Hearn will insert a rematch clause into the contract, which will be activated automatically should Joshua lose.