The Daily Mail reports that Spurs scouts have been watching the 17-year-old since last season.
Jovic has scored three goals in the first four games this season and is also being tracked by the likes of Arsenal, Chelsea, Ajax and Benfica.
Reports claim Red Star value the Serbia Under 18 international at around £6million.
Red Star director Zvezdan Terzic has previously compared Jovic with Radamel Falcao.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.