The veteran midfielder will leave Camp Nou for Al Sadd at the season's end and has already crowned his final season at the club with the domestic double.
However, Puyol wants to see his former colleague triumph in Europe against Juventus on Saturday before he leaves the continent for Qatar.
"I really hope he can do it," he told Sport.
"I'm confident in the team and it'd be a great image for him to finish his time as a Barca player.
"Xavi has lifted trophies as captain, but I hope he can lift the Champions League, which is different."
Puyol was Barca skipper in 2011 when the club won their last Champions League and famously let Eric Abidal, who had just recovered from cancer, lift the cup.
"He had fought very hard and had shown us that you always have to fight. He deserved it. It takes a lot to explain what it feels like when he lifts the cup."
Barca and Juventus meet in Berlin at 20:45CET on Saturday.