Taylor's split-decision win over Jack Catterall in his undisputed junior welterweight title defence although it was deemed highly controversial.
The 'Tartan Tornado' - the UK's first four-belt undisputed champion - produced a flat performance but the scorecards read 114-111, 113-112 for Taylor and 113-112 for Catterall.
Taylor has since vacated his WBA belt while the WBC is ordering him to take on mandatory challenger Jose Zepeda.
Meanwhile, the WBO have not ordered a rematch between Taylor and Catterall, instead placing 'Gatto' third in the rankings behind Jose Ramirez and Liam Paro.
While a rematch would not have all four titles on the line again, promoter Ben Shalom insisted both fighters want the fight although it'll be 'difficult' to make.
"I think both fighters do want the fight but the problem is maybe with different promotional companies right now and that can sometimes make things difficult but we'd love to see the fight happen.
I think Jack deserves it. But at the end of the day, it will be what Josh wants as well," Shalom exclusively told Planet Sport. "He has many options, but we always felt very aggrieved by the first way and whatever happens.
"We want Jack to have an amazing career off the back of it and get all the opportunities he deserves.
"Maybe that will be the rematch but whatever happens I think he deserves another world title shot.
"I speak to Top Rank and Josh a fair bit. I know that he wants the fight but I also know that if this thing's in the way of him getting the fight, he's not going to hang around.
"It's just Top Rank promotional company and they'll decide what's best for him. I think everyone wants that fight but it might be a difficult fight to make. I don't know. I hope it happens. That's all," said Shalom.
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