The Inter Milan starlet has been attracting attention from some of Europe's biggest clubs with Madrid now the latest to turn their head.
Inter Milan have been thus far reluctant to lose the 20-year-old and it is understandable given Kovacic's great talent and potential.
Liverpool have been credited with an interest recently but they could get gazumped by Real who appear to be starting their summer recruitment in earnest.
According to usually reliable Italian football journalist Gianluca DiMarzio, Madrid transfer guru Jose Angel Sanchez held a meeting with the Croat's agent and his Italian representative Mario Mamic and Beppe Bozzo respectively.
And this apparently after manager Carlo Ancelotti gave his blessing to the potential signing leaving Los Blancos ready to bid in the region of €20-25 million.
Such news will demonstrate that they are very keen on the Austrian born midfielder and that Inter may be tempted to do business if the price is right.
Where Kovacic fits in exactly is anyone's guess given the quality already Madrid's squad but one thing is for sure, the Nerazzurri would be mad not to delay negotiations until after the World Cup.
For Kovacic is likely to be a key performer for Croatia and thereby naturally increase his value to Inter who would stand to make even more money from any sale to the Champions League winners as a result.
That aside generally incoming players as young as Kovacic do not get much of a chance at Real regardless of the price tag so his career may be better served by staying at the San Siro where he can continue his footballing education in what is already one of Europe's top leagues.
As far as Liverpool are concerned they have sufficient alternative options such as Adam Lallana and Xherdan Shaqiri to warrant any defeat to Madrid in the chase of Kovacic not the end of the world.
The only problem is the Reds have been unable to close out any of those deals as they continue to drag on for weeks on end. Who is to say these targets are not swiped from under Liverpool's noses as Kovacic could be.
If that were to happen an inquisition would need to be undertaken into how the club operate in the transfer market following the failure to sign high profile players such as Diego Costa, Willian, Henrikh Mkhitaryan and Yevhen Konoplyanka in the past.