Barca are currently regarded as the best club side in the world, and have won three La Liga titles, a Copa del Rey and the UEFA Champions League twice in the last three seasons.
Bayern, on the other hand, are the most successful side in Germany but had a campaign to forget last term as they were pipped to the league title by Borussia Dortmund.
However, since the introduction of Juup Heynckes at the helm of the club, Bayern have recovered their dominant form this season, and Neuer believes that on their day, they are as good as Barcelona or Real Madrid.
"Our chances in Europe have a lot to do with form on the day," Neuer said on Bayern's official website.
"We've turned in a number of good displays in the Champions League. If we can repeat that or even improve it, we're on a par with Barcelona or Real Madrid."
And while the Champions League remains a realistic target for Bayern this season, winning the Bundesliga is still Neuer's number one priority.
"I want to win the league at last," Neuer added. "Even if some of the lads who've been here for awhile and who've frequently laid hands on the championship shield might not want to hear it."
Bayern are currently top of the Bundesliga and meet Swiss side Basel in the knockout round of the Champions League.