Madrid booked their place in the last-eight of the competition after defeating Malaga 4-2 on aggregate following Tuesday's 1-0 victory at La Rosaleda in the second leg.
Barca are yet to confirm their spot against Jose Mourinho's team but are heavy favourites to progress as they hold a 4-0 lead over Osasuna from the first leg ahead of Thursday's return game in Pamplona.
"Barcelona must still play [the second leg against Osasuna on Thursday] but we are ready and we will approach the next stage with a lot of respect," Alonso told AS after their 1-0 win at Malaga.
"I do not want to compare [both clubs].
"We have been doing well, we have started 2012 with three victories and we are not concerned about what happens elsewhere.
Madrid were on course for the quarterfinals courtesy of a 3-2 lead after last week's first leg, and they wrapped up an aggregate 4-2 victory thanks to Karim Benzema's 72nd-minute goal.
Speaking on the game, Alonso said it was important that his team-mates approached the game with a winning mentality as opposed to going for a draw, which would've also seen them through.
""We wanted to win the match," he said.
"We controlled the game and had chances to score, and although our goal was a bit lucky, we deserved it."
Madrid coach Mourinho was also full of praise for the team's battling qualities after Tuesday's win calling it a "great effort".