"In Marc and Manuel, Germany have two very good goalkeepers, but I think Manuel is a class above," Ulreich told Sky.
Neuer will be in goal when Germany take on the Netherlands in their opening Euro 2020 qualifier on Sunday, and Ulreich said that he should remain as first choice goalkeeper until the tournament next summer.
"He is just a brilliant keeper, and I think it does the team good to have such an experienced player between the posts," he said.
Ulreich kept goal for Bayern for much of last season while Neuer recovered from a series of foot injuries.
Since returning to full fitness last summer, Neuer, 32, has regained the number one shirt for both Bayern and Germany.
Yet in the national team, Neuer is under threat from 26-year-old Barcelona keeper ter Stegen.
"I want to apply pressure, and I want to push through a change in the number one spot," ter Stegen told streaming service DAZN earlier this month.
Having sent Neuer's Bayern team mates Mats Hummels, Jerome Boateng and Thomas Mueller into international retirement as part of a transition to the younger generation, coach Joachim Loew is under increasing pressure to promote ter Stegen.
"I hope the manager puts his trust in me for important games," ter Stegen told RTL after Germany's 1-1 draw with Serbia last Wednesday.
Last week, Loew confirmed that Neuer will remain his number one, but said that ter Stegen was "world class" and would get chances to play in the year ahead.
"I think we are lucky to have two such great goalkeepers," said Germany and Real Madrid midfielder Toni Kroos on Saturday. "You can't really make the wrong decision when picking one or the other."