A working date for Parker v Fury is April 1, but that could change if the bout is held in the UK.
Duco's David Higgins told the Herald on Sunday today that while he and Parker appreciated the sentiments of WBC world champion Deontay Wilder, an American who said recently he was targeting Parker's WBO title as he begins his attempt to unify the division, Englishman Joshua loomed larger in Parker's sights.
"Beating Hughie Fury will raise Joseph's status in the UK quite markedly and it would probably make more sense to target Joshua next rather than Wilder," Higgins said.
"The UK is such a big heavyweight market at the moment, with Joshua, David Haye and Tyson Fury... so that is the direction we would probably go in.
"We could look to fight Wilder at the end of the year or early next year."
Joshua, the IBF world title holder, will fight former champion Wladimir Klitschko in front of a crowd of 90,000 at Wembley Stadium on April 29.
Parker, who enjoyed a break in Samoa and New Zealand after his win over Ruiz Jr, said before he left that he would be comfortable fighting Fury in England.
"I have fought in America twice, Germany, Samoa, it doesn't matter where the fight is I'll be comfortable fighting anywhere," he said.
"This could be the perfect lead up to those bigger fights."
Wilder, who fights Gerald Washington in Alabama on February 25, predicted a win for Parker over Fury, telling Ring TV: "I want Joseph Parker. This is how I want things to go and this is what my team has in mind as well - 2017 is all about unifications.
"I'm not looking past Gerald Washington. But I look through it. I'm window shopping. After Gerald Washington, we're going after the winner of Hughie Fury and Joseph Parker, which I'm predicting Joseph Parker to win. So, I'm going after Joseph Parker for the WBO title."