The midfielder has spent the past 18 months on-loan at Heerenveen.
"I do not know what is going to happen, but if nothing happens, I will do the preseason with Madrid and it will be a good opportunity to show what I can do," he told NTB.
But a return to Heerenveen has been ruled, as Odegaard considers it "a closed chapter".
The Norwegian midfielder was enthusiastic about Real Madrid's Champions League final triumph.
"It's great, three years in a row, there's no doubt who is the best," he said.