Wanchope, who played for City between 2000 and 2004, believes the Premier League outfit have enough quality to cause an upset and overturn their 2-0 first leg defeat at Camp Nou on Wednesday.
With Barca having lost two of their last three La Liga matches, the Costa Rican says City can take full advantage of their indifferent form and send the four-time European champions out of the competition.
"They (City) are capable," Wanchope told Perform. "They are capable to do it, plus Barcelona are not playing the best football now.
"I mean, they are good players but they are having a little bit of problems and I do think Manchester City can do it.
"I imagine it would be great. If they get through Barcelona I think they can go all the way and win the Champions League."
Even if City fail to overcome Gerardo Martino's men, Wanchope believes they can still add the Premier League trophy to their League Cup success this season.
"If they don't go through they still have something to play," he added. "They still have the Premier League.
"They need to try and when you have good players, they are capable to do anything and they are capable to bounce back from failure.
"They have quality players but also you see Chelsea, you see Arsenal and Liverpool are doing well, but at least they need to win something this year.
"It could be Premier League, but they won the League Cup, and they are still alive with the Champions League so I think they, of course, need to win something during the year because of the quality of players."
