Zivkovic shone in Serbia's shock triumph at the Under-20 World Cup in New Zealand in June and, according to his agent, has drawn the interest of Chelsea and Valencia.
"We're going out of our way to keep Zivkovic beyond next June and sign a new two-year deal," Popovic told daily Vecernje Novosti on Monday.
"The board recognised instantly that he is a gem and we’ve already turned down plenty of offers from other clubs, whose agents keep calling us every day.
"He is a fine lad with a great attitude and has all the prerequisites to become a world class player."
The 19-year old Zivkovic produced a blistering performance in Partizan's 5-3 aggregate defeat of former European Cup winners Steaua Bucharest in the Champions League third qualifying round.
He scored one goal and set up two as the Serbian title holders closed in on what could be only their third appearance in the group stage of Europe's premier club competition.
(Reporting by Zoran Milosavljevic in Belgrade; Editing by Amlan Chakraborty)
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