The teen midfielder has been compared to Barcelona superstar Lionel Messi and Real Madrid playmaker and international compatriot Luka Modric.
Like Modric, Halilovic is a product of the Dinamo Zagreb youth academy, and the 16-year-old has already featured for the club's first team, becoming the youngest scorer in the process.
Halilovic is valued at £12m, but the Daily Mail reports Manchester United and Manchester City are weighing up offers in the region of £6m for the centre midfielder.
The teen sensation only signed his first professional contract with Zagreb in the summer, and made his debut last month, before scoring two weeks ago in his side's 4-1 victory over Slaven Belupo.
Halilovic has caps for Croatia under-17's, and is widely tipped to be one of best youth products ever to come for Croatia.
Manchester City have said they intend to place greater focus on youth development, insisting their big-spending days are essentially over.
As such, Roberto Mancini could be tempted to invest a modest amount in Halilovic in the hope that City can bring the best out of the midfielder, helping him to blossom to his full potential. City already have one of the most talented young playmakers in the shape of Denis Suarez.
But Manchester United and Real Madrid provide stiff competition for City. Sir Alex Ferguson has been linked with a number of centre-midfielders in the past, but Halilovic would not be a short-term solution.
The Old Trafford club lost Paul Pogba, their most promising young midfielder, to Juventus in the summer, but Halilovic could be an even bigger talent than the Frenchman, and United will be keen not to miss out should he become available.