Eberl revealed that Bayern have already held positive discussions regarding Gordon, who could be allowed to leave Newcastle United if a suitable offer is made.
“We had a very good conversation and hope to progress further,” Eberl said.
The England international, 25, is reportedly valued between €60 million and €90 million and remains under contract at Newcastle until 2030.
Bayern Munich are also tracking 16-year-old Hertha midfielder Eichhorn, who is attracting interest from several European clubs.
The teenager has a release clause believed to be between €10 million and €12 million, making him one of the most highly valued prospects in German football.
Eberl acknowledged Bayern’s interest but stressed that no final decision has been made.
“We would not be doing our job if we didn’t look at players like Kenny Eichhorn,” he said.
“Whether it happens depends on many factors.”
Bayern are expected to be active in the transfer market as they refine their squad for the upcoming season.
However, Eberl declined to comment on other defensive targets such as Josko Gvardiol, of Manchester City, or Eintracht Frankfurt's Nathaniel Brown, signalling negotiations are still in early stages across multiple profiles.
The club’s recruitment strategy continues to balance established Premier League talent with elite teenage prospects from the Bundesliga pipeline.