AS says United boss Jose Mourinho is monitoring the 23-year-old Croatia international, who is yet to establish himself as a first-team regular despite being in his third season at the Santiago Bernabeu.
Kovacic has made just seven La Liga appearances this term and fancies trying his luck elsewhere.
Tottenham are also said to be keen on snapping up the ex-Inter Milan star.
However, the report adds that Real do not want to sell Kovacic this summer. But if Real chiefs decide to usher in a fresh era with a new manager, Kovacic could finally become central to their plans.