Arsenal are close to working out an agreement to sign the Real Madrid midfielder on a permanent transfer this summer.
The two clubs are in advanced negotiations for Odegaard to join the Gunners and the deal is expected to be ratified for a fee of €40m.
Arsenal and Real Madrid are believed to be finalising the structure of the deal and the Norwegian is soon expected to fly out to London to complete the move.
According to Spanish radio station Onda Cero, as part of the broad agreement Real Madrid have secured the right to first refusal if Arsenal decide to sell the midfielder in the future.
Real Madrid will have the option to match any transfer fee that Arsenal are offered for the Norwegian if they decide to sell him.
Odegaard spent the second half of last season on loan at Arsenal and Mikel Arteta was open about wanting him back in the summer.
Arsenal are pushing to complete the deal to sign the midfielder in time to have him in the squad against Chelsea on Sunday.
Odegaard has been keen to move on from Real Madrid once he realised he was unlikely to get the minutes he craved under Carlo Ancelotti this season.
