Reports in Italy suggest Dinamo Zagreb refused Madrid's opening offer for the 16-year-old wonderkid. Halilovic has been dubbed the 'next Messi' after the youngster burst onto the scene becoming the club's youngest ever scorer earlier this month, but the Croatian youth international has played down the comparisons.
The teen centre-midfielder has also been compared to Madrid's most recent big-money signing, Luka Modric. The former-Tottenham playmaker came through the youth ranks at Zagreb, just like Halilovic, and Madrid boss Jose Mourinho is thought to want the 16-year-old alongside Modric at the Bernabeu.
But Manchester United have also been credited with an interest. Sir Alex Ferguson was a long-term admirer of Modric when the Croatian international was playing at Tottenham, but ultimately missed out on the diminutive playmaker. He's believed to not want to make the same mistake twice, and is thought to be keen on Halilovic.
Manchester United have an excellent record of bringing through young stars into the first-team, but in recent seasons that reputation has taken a knock.
Ravel Morrison and Paul Pogba, two of the Manchester United academy's brightest prospects, both ran into disciplinary trouble, and were eventually moved on from Old Trafford.
Manchester United take on Stoke City on Saturday, as they look to bridge the gap to league leaders Chelsea. Roberto Di Matteo's side currently sit four points clear of United at the top of the Premier League.