The 22-year-old attacking midfielder has been left frustrated by his lack of game time at Real Madrid this season and wants to leave the club this month.
Real Madrid are prepared to let him go this month, but only on a simple loan deal with no option to buy as the club believe that he still has a future at the Bernabeu.
Several clubs are chasing the attacking midfielder’s signature and Arsenal have also been in talks with Real Madrid over signing him on loan this month.
But according to Spanish sports daily Marca, Real Sociedad are Odegaard’s preferred choice of club if he leaves Real Madrid in the next two weeks.
The Norwegian had a successful loan spell at Real Sociedad last season and scored seven times in 36 appearances for the club.
Several other clubs in Europe are also interested in him, with even Ajax throwing their hat in the ring for a loan move.
But for the moment, Real Sociedad have the edge because of the player’s will to join them this month.
Real Madrid also feel that the Norwegian would be best served joining La Real in the ongoing transfer window.
The two clubs have been in talks over agreeing on a loan deal for Odegaard.