Per Eurosport Norway (h/t Marca), the 20-year-old explained the Madrid giants have commended him on his performances, but he added he is keen to complete the duration of his loan deal at the Anoeta Stadium:
"I am in contact with Real Madrid, as sometimes they write to me to tell me how they see me. They have congratulated me and praised my good start in the league. They have told me that they are happy with me. The idea is to respect [the loan deal]. I am happy at the team, and so I want to continue here until my two years end."
Odegaard joined Los Blancos as a 16-year-old from Stromsgodset in 2015 amid much fanfare after trialling with numerous top European clubs, including Liverpool, Bayern Munich, Manchester United and Manchester City.
He failed to settle in Real's Castilla side, though, or to establish himself in the first team.
The Norway international was subsequently sent out on loan to Dutch sides Heerenveen and Vitesse Arnhem, before starting his spell at La Real in July.
Odegaard has made a big impact in La Liga at the start of the 2019-20 campaign, netting two goals and providing two assists in eight appearances:
It is perhaps no surprise he was unable to immediately live up to the huge hype surrounding him when he arrived at Real given he was so young.
In a couple of seasons out of the Spanish spotlight, though, he has been able to progress away from the pressures of the Bernabeu and the wild expectation on his shoulders.
On the evidence of how he has started life at La Real, that has done him a huge amount of good, and Odegaard may yet live up to his enormous potential.
Real should still be wary of recalling him too early, however.
But if they allow him to continue to advance away from the Bernabeu, Real may yet get the player they hoped for back in 2015, as Odegaard is increasingly showing he could be a superstar in the future.