Joshua made the first defence of his IBF heavyweight title by stopping Dominic Breazeale at the 02 Arena in Wembley on June 25.
It had been reported that Joshua was set to box in Manchester on November 26 but his promoter Eddie Hearn has revealed he could take top billing on a busy night of heavyweight boxing in Wales instead.
Hearn has also hinted that Kubrat Pulev has emerged as Joshua's most likely opponent despite suggestions the likes of Bermane Stiverne and Parker, the mandatory challenger, were also in the mix to face him.
Hearn hinted Parker could face David Price as part of the card in the Welsh capital.
'We are talking maybe about David Price v Joseph Parker, Dillian Whyte v Dereck Chisora and then Anthony Joshua v Kubrat Pulev all bundled into one - it could be a lot of fun," he said.
'It could be either late November or in December - we will definitely have the roof shut given the time of the year!'
Talks regarding a clash between the two London-based heavyweights Chisora and Whyte have already taken place between Hearn, who promotes Whyte, and the Sauerlands, who promote Chisora.
The two boxers have traded insults on social media and fuelled the interest in a fight when they clashed at a press conference in London's trendy Chelsea Harbour earlier this year.
Now they could be set to finally collide as chief support to Joshua, who will also get the chance to meet Parker ahead of a likely showdown with him early next year.
The 20-0 Auckland puncher, who is currently No 1 with the IBF, is being lined up for an intriguing clash with Liverpool favourite Price, who continues to rebuild under the tutelage of Dave Coldwell.
However Joshua will not be able to take his eye off the ball should Pulev be confirmed as his opponent.
The Bulgarian, whose only defeat in 24 fights came at the hands of Wladimir Klitschko, would clearly represent the toughest test of Joshua's professional career to date.
The former European champion, 35, was knocked out by Klitschko in 2014, but is back on track after winning his three fights since - most recently against Chisora in Hamburg in May.
Hearn added: 'There are some big plans and maybe in two weeks' time they will all be unveiled.'
-Staff reporters and Daily Mail