Joshua, who is the reigning WBA and IBF world heavyweight champion, is in for a busy 2018.
Three fights have been lined up for the Watford-born star as he sets his sights on unifying the division.
A showdown with New Zealander Parker has been in the pipeline for some time.
And according to the Sunday Star, Parker will be Joshua’s first opponent this year on March 31.
The report claims Joshua will earn as much as £15million from the fight.
Anthony Joshua is likely to fight Joseph Parker next (GETTY?)
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“I don’t think it’s going to be that hard. If I have to go to England, then so be it”
Should a deal be finalised at a meeting between Parker’s promoter, David Higgins and Eddie Hearn, then Parker will fly to London to hold a press conference with Joshua.
The Principality Stadium in Wales is expected to be the most likely venue, but nothing has been confirmed yet.
Joshua stopped Carlos Takam under the Principality’s closed roof back in October.
Twickenham and Old Trafford have also been considered.
Joseph Parker could face Anthony Joshua on March 31 (GETTY)
Meanwhile, Deontay Wilder is confident a deal to fight Joshua shouldn’t be too difficult to arrange.
He said: “I don’t think the business side is going to be that difficult, especially after I beat Luis Ortiz and I knock him out.
“I’m not worried about traveling. But is he worried about travelling?
“He’s never traveled, and he ain’t planning on travelling. I like to travel.”