There has been bad blood between Taylor and Catterall, 29, since the controversial points win for the Scot, with negotiations about a re-match ongoing.
Catterall, part of Eddie Hearn’s Matchroom stable, has won both his bouts since the loss to Taylor in Glasgow by split decision.
And Taylor, with Bob Arum’s Top Rank, is keen to reassert himself having been dethroned as undisputed light welterweight champion two years on from winning all four belts in his win over Jose Ramirez in 2021.
The loss to Lopez at Madison Square Garden was the first of his professional career.
“Hopefully, that’s the one we’re trying to get done,” Taylor told BBC Scotland. “I just want to shut a lot of people up and put that bad performance [against Catterall] to bed, and put that doubt to bed.
“They did put in an offer but my promoters didn’t put it to me. They said ‘we’ve had an offer and said no’. They told me it was just about an 80% pay cut.
“They came back with another offer which was essentially the same offer but taking away the American rights. Which means they were giving me the same money but my promoter would have to put in the rest of the money for their show.
“I just want to fight. And Eddie Hearn is in interviews saying it’s a big fight, a huge fight. So it’s like you’ve got to be realistic about what you’re going to pay the fighters.
“I’m waiting for all that to be sorted out. I really want to get that one done first and see what’s happening with fights further down the line.”