The 22-year-old has taken to life in North London like a duck to water and has quickly become a fan favourite following a string of impressive performances under Mikel Arteta.
The Norwegian has now joined up with his international colleagues ahead of crucial World Cup qualifiers against Gibraltar, Turkey and Montenegro.
"Haven't thought about what'll happen in summer. Deal with Arsenal is until the end of season. We'll see what happens this summer. I've said things before that I still stand for: Stability and development are key words."
Luckily for the Gunners, stability and development are two things that the former Strømsgodset midfielder has enjoyed since joining from La Liga, with Ødegaard featuring in all but one of Arsenal's fixtures since his arrival in January.
Additionally, Ødegaard has benefitted from a positive relationship with Arteta and has frequently spoken highly of the Arsenal manager, claiming that the pairs relationship is "Very good. He is incredible. I have a lot to learn from him. I just need to 'sharpen my ears' and pay attention. He is fantastic."
Astonishingly, Arsenal's number 11 has played more minutes for the Gunners than Real Madrid's first team, which is a factor he will no doubt take into consideration when determining the best course of action for his future.
When asked about his time at the Emirates so far, Ødegaard said: "It's been improving from the very beginning. I feel I quickly adapted and understood how we play.
"I lacked match fitness and self-confidence. The more games I've played, the better I've become. It's a rising curve."
It remains to be seen whether or not Real Madrid President Florentino Perez will entertain the idea of Ødegaard extending his stay at Arsenal on a permanent basis.
However it is believed the presence of current Los Blancos boss, Zinedine Zidane, will be a determining factor as the former Juventus playmaker has been reluctant to hand first team opportunities to Ødegaard thus far.