The Sun says City have spent the last year monitoring the winger and in March they opened talks with the Serbian club over a possible move.
Radulovic first caught City's eye last year when he scored in a 2-0 victory over Tottenham Hotspur in the UEFA Youth League.
Spurs have also been tracking him since but City would be clear favourites to sign the 18-year-old this summer should a move go ahead.
Despite his promise though he would not be expected to gain a place in Pep Guardiola's side straight away.
City would likely loan him back to Red Star or one of City's affiliate clubs from around the world.
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