A goalless draw with Benfica leaves Barcelona in a tricky spot in Group E
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Nonetheless, Laporta declares he is "convinced" Barcelona will reach the last 16 with a famous victory masterminded by their "very strong" manager Xavi, who was appointed earlier this month.
"Beating Bayern is something that can be achieved," Laporta told Diario AS . "There is going to be a miracle, I am convinced that we are going to win.
"Xavi is very motivated and very strong. I hope everything goes well for us, I think that at the moment Xavi's arrival has generated a little respect from our opponents. They know we can do it again."
Although Barcelona's chances of victory in Bavaria appear slim, Xavi could have a wildcard up his sleeve as Ansu Fati – who has four goals in eight games this season – may return from the sidelines in time for the clash.
The forward, 19, suffered a hamstring injury in early November but Laporta anticipates he could feature against Bayern.
Asked about Fati's condition, he responded: "With Ansu? It may come, the doctors will appreciate it."
Meanwhile, Xavi was unimpressed by his side's performance against Benfica and will demand a much-improved display against Villarreal on Saturday and Bayern next month.
Joan Laporta is confident Barcelona will reach the Champions League last 16
"We were far superior to Benfica and we played a great game, we only missed the goal," the Spaniard said. "If we had scored, we would be talking about a great game.
"I'm still optimistic. We're Barca, we have talent and players to make a difference. But today we added one point and that's not Barca worthy.
"Today we have seen that there is no physical issue. What we must do is regain the confidence of the players who can score goals. We will see what we can do on the market in January."