While Real Madrid are regarded as favourites for the Belgium goalkeeper, AS says former club Atletico are also monitoring his situation.
Should they lose Jan Oblak this summer, Atletico would use the money raised to compete with Real for Courtois.
This week, Courtois admitted he missed Madrid, where his family now live.
He said: “My personal situation is related to the city of Madrid, my two children live there with their mum.
“I have my daughter every day on FaceTime, she often tells me that she misses me, while my son is still too small to communicate like that.
“Whenever I have the opportunity, I try to return to Spain. As a situation, it is not always easy.
“Yes, my heart is in Madrid. It is logical and understandable."