The winger is considered one of the best prospects in Europe and the 17-year-old has no shortage of admirers with Ajax ready to do battle with the Reds for his signature.
Much could depend on Liverpool's efforts to land a Champions League place but Ajax Sporting Director Marc Overmars has confirmed the Dutch giants are ready to battle Rodgers for his signature.
"He is an interesting player that we are following," Ajax Sporting Director Marc Overmars told the Dutch media.
"Thinking about possible reinforcements for next season, our preference is for Dutch players."
Newcastle and Manchester City are among other clubs to have expressed an interest in Zivkovic, who appears destined to leave Groningen in the summer.