The player himself wanted to return to Real Sociedad, where he impressed on loan last season.
"They are sixth in the table, three points off the top four. If they think they are fighting for the same thing, which is Champions League qualification, then it doesn't make sense to strengthen a rival."
After returning to the Bernabeu in the summer following his Real Sociedad loan, it seemed Odegaard might become a first-team regular under Zinedine Zidane, who coached him in the B team when he first joined the club in 2015 and is now in charge of the senior side.
But after starting the first two La Liga games of the season, the attacking midfielder has featured only once from the outset of a league game since - on 21 November.
"The player preferred to go there because there would be no need for adaptation and he just wants to play. But Real prefer Arsenal because of the style and because they believe he will play there regularly as well.