Eberl said talks with City, who won their first Champions League title last month, were under way for a possible move of the Croatia international.
"Josko and his advisors have submitted the wish to us for a transfer to Manchester City," Eberl told Leipziger Volksnachrichten newspaper.
"We are in talks with Manchester. There is nothing more to say about it at this moment."
The back-to-back German Cup winners have seen several top players leave with Hungarian midfielder Dominik Szoboszlai's move to Liverpool on Sunday being the most recent one.
Defender Konrad Laimer has moved to Bayern Munich while France international Christopher Nkunku has joined Chelsea in the Premier League.
"I can understand the disappointment and concern of the fans," Eberl said. "No club and no coach in this world wants to lose players of this calibre."
"But we have been prepared for this and I can promise that we will have once more a good and exciting team."
Leipzig, who finished third in the Bundesliga and will compete in the Champions League group stage, have brought in attacking midfielder Christoph Baumgartner and talented 20-year-old Slovenian Benjamin Sesko among others.
"We have already signed some good lads and will bring in more and exciting players," Eberl said.
