The Catalan club were drawn against City in the last 16 for the second consecutive year on Monday after finishing top of Group F.
Last season Barca claimed a 4-1 aggregate win over Manuel Pellegrini's Premier League champions and may well be favourites to progress to the quarter-finals again this time around, with City just scraping through their pool.
But Zubizarreta is anticipating a strong challenge from a City side that overcame both Bayern Munich and Roma in their final two group games to advance.
"It is the same draw we had a year ago, it was a very difficult game and we are going to look forward to it," Zubizarreta said.
"Manchester City have an outstanding squad with a very good coach, a very good team and are very competitive.
"We know all about them. They have been playing at a very high level and it is going to be difficult. Two great teams with incredible players and anything can happen.
"Can we go further than last year? Hopefully we can go all the way."
