Don Balon says Guardiola has shown a keen interest in the German international.
Bitter rivals Manchester United have been linked with Kroos over a number of transfer windows.
And if Real give the 28-year-old the green light to leave, expect the two clubs to fight tooth and nail for his signature.
Guardiola is prepared to outlay over £60m for Kroos.
The German impressed in the Champions League final win over Liverpool which saw Real win the tournament for the third straight campaign.