The 31-year-old Scottish undisputed super-lightweight world champion clashed with his English rival at the OVO Hydro in Glasgow two weeks ago after a heated build-up to the clash of ‘The Auld Enemy’.
And Taylor, who was fighting on home soil for the first time since 2019, came on strong against Catterall in the later rounds to secure the victory.
However, the fight was not without controversy, as many felt it should have gone the other way.
Speaking to Sky Sports, Taylor said: “You know, fair play to Jack, he got great tactics, great game plan, came in and executed it well, but I still think I did just enough to win the fight.”
Asked if Catterall deserves to fight for the world titles again if he vacates them in the future, he added: “Yeah, of course, I think he deserves it.
“Yeah, I think he deserves it.
“You know, we’ll see what happens down the line, we can have that fight again with Jack.
“Why not? Like I say, I’m open to it, and we’ll see what happens in the future.”
Taylor added that he is willing to face Catterall again in the future if his one condition is met.
He continued: “Most likely probably at catchweight.
“I just I can’t make the weight anymore safely I don’t think so yeah we’ll see how it goes.
“But yeah I’m game for a rematch or whatever yeah.”
Promoter Ben Shalom, who co-promoted the show with Top Rank, has also insisted that ‘it makes more sense at a catchweight’.
Shalom added: “I think it’s difficult. I know Jack would do anything for a rematch.
“I think maybe it makes more sense at a catchweight, at 143, or 144, particularly if there’s not going to be titles on the line.
“But yes they can fight again. I do think that is a route forward. Jack, there will be vacant world titles there for him, if Josh moves up and I’m sure he’ll get his opportunity again.
“But let’s not get away from the fact that Jack just fought for all four world titles, for a life-changing amount of money to come from it and opportunities to come from it.
“It happens extremely rarely so rematch or not, Jack has just lost something that he’s worked his entire life for.
“We’re going to push the rematch. We think that is a viable option, but we think it should happen at a catchweight.
“At 143, 144, that allows Josh the extra weight he needs, but is also fair on Jack, because really he fights at 140 and should continue to do so.”