The Norway international has made a promising start to life at The Emirates since having signed for the Gunners from Real Madrid on loan in the January transfer window.
Odegaard, 22, has been a regular fixture in the first team at the north London side and has been earning lots of praise for his performances for Mikel Arteta’s men.
As things stand, Odegaard will be heading back to Real Madrid at the end of the current campaign.
However, former Arsenal star Winterburn believes that the Gunners will want to consider signing Odegaard on a permanent deal this summer, and he feels that there is space for both the Norwegian and Emile Smith Rowe in the squad.