Both Bayern and Liverpool are chasing after Alonso, as they want him to replace Thomas Tuchel or Jurgen Klopp respectively.
"Of course we want the new coach to be chosen as quickly as possible, but it has to be right, there won't be a quick fix," Eberl told Sky Germany. "We have a list of priorities that we want to work through. But we still have one more season with Thomas Tuchel.
"We want to finish in the best possible way. That's why I've often spoken about the balancing act and that's what we have to do."
"It's not my place to talk about other coaches," Eberl added.
"We have to keep our jobs and find out who is the right one. Then we have to see what it can cost and whether we can afford it.
"There are many facets that play a role when looking for a coach. We haven't spoken to anyone yet. It will always be respectful because one or two candidates have another club, so it's not that easy."