The 18-year-old stole the show on Sunday as he helped the Catalans beat rivals Real Madrid 3-1 to clinch the Spanish Super Cup title.
Gavi scored a goal and provided two assists as Barca outclassed Los Blancos.
Xavi was delighted with the performance and had special words for Gavi, who has unlimited potential according to the Blaugrana head coach.
"Gavi is a boy that thrills us all when we see him competing like this," said Xavi.
"He puts his soul, his heart and his character on the pitch and transmits it to the rest of the team, and he is just 18.
"He was gifted with leadership skills. He projects that courage and that rage when he plays football and it's something special to see.
"I already said this many times but I never get tired of praising him. Hopefully, he will never stop like this, because he has no limits."