The 19-year-old has been impressive for Partizan Belgrade this season.
The 19-year-old has been hugely impressive for current side Partizan Belgrade this season, scoring seven goals in 15 league games. However, L'Equipe reports that he will be available for around £3.75m, which appears to have grabbed attention elsewhere.
Bundesliga side Borussia Dortmund and Ligue 1 champions Paris Saint-Germain are also keen on Zivkovic (via L'Equipe), who was part of the Serbia side that won the under-20 World Cup last year. The youngster scored two goals along the way, including the opener during the semi-final victory over Mali.
Since then, Zivkovic has graduated into the Serbian national side, and it appears that in the near future he may well be on his way to the Premier League should either the Reds or City win the race for his signature.
If both clubs are keen on a move, they may well be using his countrymen to tempt him towards their respective sides. Marko Grujic joined the Reds from Red Star Belgrade earlier in the window, while Lazar Markovic also remains on Liverpool's books. Meanwhile, Serbia's vice-captain is Manchester City stalwart Aleksandar Kolarov.