Back in February, Catterall challenged Josh Taylor for his world titles in the 140lb division.
It was clear to see (for most) that the challenger did more than enough to win in Glasgow, but he lost in controversial fashion via split decision.
Taylor was scheduled to face Jose Zepeda in a mandatory defence next, but the Scotsman has vacated his WBC belt to pursue the Catterall rematch.
After signing Catterall, BOXXER promoter Ben Shalom has confirmed that a fight against Taylor is on the agenda.
"We can hopefully make Catterall-Taylor II," Shalom told Sky Sports.
"You saw the reaction on the night. The rematch had to happen, it was so unfortunate for Jack.
"So we've got a serious fighter on our hands and a serious fight as well."
Catterall is eager to "go and settle" his dispute with Taylor and become a world champion in the process.
"I'm super excited," Catterall told Sky Sports. "I think this next stage of my career now is vital, and I believe with BOXXER and Sky Sports that I will be crowned world champion in the future.
"I'm looking forward to getting the green light, getting back in training camp and going and challenging for those world titles.
"Yeah definitely [a rematch with Taylor]. We all saw the controversy over the last fight, and there's definitely something to put to bed with Josh.
"Hopefully that fight can be made in the future and I would look to do the job properly this time and put it to bed."
Catterall added: "Ultimately, I would love to get that fight again and go and settle it.
"Hopefully that can be done sooner than later, but the main focus is me now and moving forward with BOXXER and Sky Sports, and getting settled into the next stage of my career."