The Norway international has been outstanding in the early weeks of the season at loan club Heerenveen.
Odegaard is in his second season with Heerenveen and is now beginning to match his reputation.
Don Balon says while happy with the glowing scouting reports, Real chiefs know they face a dilemma over the midfielder's future.
The arrival of Spain U21 star Dani Ceballos from Real Betis appears to have blocked the path for Odegaard to return to Madrid. The youngster was already facing an uphill battle with Isco and Marco Asensio emerging last term.
Further complicating the situation for Odegaard is Real coach Zinedine Zidane. The pair worked together with Castilla, where Zidane failed to be won over by the Norwegian teen.