Gladbach are set to lose income from broadcasting, sponsorships and ticket sales during the Covid-19 outbreak with all Bundesliga matches suspended until at least 2 April.
"The team has offered to forego salaries if it can help the club and its employees," Eberl told the club's website.
"I didn't have to explain much. The players know what's going on. It's their job, they have already informed themselves and thought about what they could do," he added.
Coaching staff and boss Marco Rose have also said they would go without their salaries.
According to media reports in Germany, the decision by the likes of captain Lars Stindl, forward Alassane Plea and goalkeeper Yann Sommer will allow the side sitting fourth in the table to save €1 million.