Barrios was upgraded from interim to full WBC champion in June 2024 and has made two successful defences via draws.
He retained his title with a majority draw against 46-year-old Manny Pacquiao in July.
Barrios has won 29 of his 33 fights, with 18 victories by knockout.
“Becoming WBC welterweight world champion was more than a moment – it was a promise to my family, my city and everyone who believed in the grind when no-one was watching,” he said.
“San Antonio built me, and every sacrifice I’ve made comes with me into that ring.”
Garcia’s meeting with Haney in April 2024 was scheduled to be for the WBC light-welterweight title, but Garcia missed weight and was not eligible to win the belt.
He has sealed 20 of his 24 victories by knockout.
In December the WBC confirmed Britain’s Conor Benn as number one in the welterweight rankings. He could be next in line to face the winner of Barrios-Garcia.
Benn said at the time he would be “watching closely”.
“I’ll be coming for that belt and Britain will have a new world champion,” he said on Instagram.
