Mikel Arteta bolstered his midfield options with the addition of 22-year-old Odegaard from La Liga giants Real Madrid on loan until the end of the season last month.
Though Arsenal do not have a purchase option included in their deal for the midfielder, they are open to the prospect of making his move permanent in the summer.
It is also suggested that Odegaard would be more than happy to commit his long-term future to the Gunners if his loan spell with the club goes well.
The Norway international is also not keen on returning to parent club Real Madrid upon the expiry of his loan contract with Arsenal if Zidane is still in charge of the side.
Odegaard struggled to clock playing time under Zidane at Real Madrid and is aware that his future at Bernabeu is uncertain with the Frenchman at the helm.
Knowing Arsenal’s openness to sign him permanently, the Norwegian could look to put an end to his Real Madrid career and join the Gunners in the summer.
However, there is no certainty that Zidane will remain in charge of Los Blancos beyond this season, with the Spanish outfit struggling this season.