The goalkeeper, who made over 100 appearances for Monchengladbach, has been signed by the Liga runners-up to replace Victor Valdes and Eberl believes the transfer is an honour for the Bundesliga team.
"We would not be happy if he is sold by Barcelona, but it would be a pretty big investment for us if it came to this," said Eberl in an interview with the Rheinische Post.
"It is natural pride, even if it hurts to lose such a player. The fact that he now plays with the greatest players in the world is an honour for our club.”
The 22-year-old has signed a five-year contract with Barcelona and was unveiled by the club in a presentation last week.
With Jose Pinto also parting ways with the club, it is not yet clear who will compete with the 22-year-old for the first-choice goalkeeper position.
Barca sporting director Andoni Zubizarreta is confident, however, that ter Stegen has the quality to be a success at the Spanish club.
"He's quick, he's agile, he is also very good in the air and has strengths in one-on-one situations,” said the retired goalkeeper. “Obviously, there is still room for improvement but he is young and has time."