Barcelona have a seven-point advantage on Madrid in La Liga, but have suffered two consecutive defeats - elimination by Manchester United in the Europa League and then a stumble against minnows Almeria.
"It's a strong Madrid, a Madrid that have won trophies recently, we are a team in the process of construction," Xavi told a news conference.
"Madrid are competing in Europe, they thrashed Liverpool at their ground, they are favourites, to be honest.
"We have the personality and players to hurt them too, we've shown it - for me it's quite an even tie."
Barcelona beat reigning La Liga and European champions Real Madrid in the Spanish Super Cup final in January, lifting their first trophy since Xavi took over in November 2021.
Despite their fine start to 2023, Barca suffered another European exit and missed the chance to move 10 points clear of Madrid in La Liga after Almeria beat them for the first time ever on Sunday.
Without injured duo Pedri and Dembele, joined by Lewandowski who suffered a hamstring strain at the weekend, Xavi said his team had to be brave.
"We have to be more of a team than ever, as much in defence as in attack, or strategically," said the coach.
"These games are decided by small details, we have to be very brave, to have personality and lose the ball as little as possible, because they can hurt you with Vinicius, (Fede) Valverde, Rodrygo, (Karim) Benzema.
"It's a game to show our model of play, as we did in the Super Cup."
Madrid coach Carlo Ancelotti said his team would not make the same mistakes as they did in that 3-1 defeat in Saudi Arabia.
"In the Super Cup game we lacked commitment, strength, we made individual errors," Ancelotti told reporters.
"Repeating these errors will affect us, but I don't think we will repeat them.
"It's a very important game, we are very close to winning a competition that is very important for us."
Ancelotti said his team was not over-dependent on the Brazilian.
"It's a positive thing, he's one of the best players in the world," added the coach.
"He decides games in our favour many times, having a dependence on him is quite normal, because at this moment, he's one of the best players in football."