Monterrey head to the Estadio Azteca on Saturday three points adrift of America in third position after 12 rounds in Apertura, though Carlos Barra's men have a game in hand.
The four-time Mexican champions have won two of their past three league matches, drawing 1-1 with Tijuana before the international break.
Antonio Mohamed's America, however, have the edge over Monterrey, who have failed to beat their high-flying opponents in six previous attempts.
"The team has to think about winning. Statistics are there and we must try to break them," said Zavala.
"Throughout the tournament we played in other places that had not won and now they have achieved triumphs.
"Team is psyched to win and claim three points. We want to be in the top rating."
Zavala added: "We know that in the end of the tournament we will play tough matches, but the team is ready.
"Now we have a tough opponent who is America that are doing well throughout the tournament and we have the chance to fight the lead with them.
"Moreover, it will be a good parameter for us."
America's three-game winning streak came to an end last time out, conceding three goals in the final five minutes as Cruz Azul ran rampant.
"We do a counter-attack goal in the last game so if you have to be careful but we were already working on it and are prepared for Monterrey," said the 27-year-old.
In other fixtures, Ronaldinho's Queretaro know there is no margin for error when they travel to Tijuana on Friday.
