The Norwegian joined the Gunners on loan in the January transfer window, and recently refused to rule out signing for Arsenal on a permanent basis.
“You never know what is going to happen,” Odegaard told Norway’s TV2.
“But for now, I am just focusing on doing my best this season and helping the team as much as possible. Then we’ll see what happens.”
His comments are said to have angered Real Madrid, who have plans for him to return to Spain full focused on playing for Los Blancos.
And now former Arsenal star Kevin Campbell has tipped the forward to leave Real Madrid in the summer window and join the north London club permanently.
He told Football Insider: “While Martin Odegaard is a Real Madrid player he has been at the club six years and has never really established himself. That is a long time.
“He probably wants a home and some stability. He has no language problems coming to Arsenal. Arteta is trying to build a good culture there.
“The dressing room is finally right and that is why Odegaard probably feels comfortable.
“There is a lot of young players coming through now as well which is great for him. He can bounce off of those guys. Why not seek a home? Why not join permanently?
“He is good enough. That is one thing that I know. He just needs the platform to show it. I can see it happening.”