But legendary forward Alan Smith is hoping the club have "done their homework" on the 22-year-old so he doesn't end up like a previous loan signing, Denis Suarez.
When asked about Mikel Arteta's interest in the Norwegian, Smith told Stadium Astro per Goal: "To have another option perhaps. I don't think he'd walk into the team by any stretch.
"He's had his problems developing at Real Madrid and the last thing Arsenal want is to get somebody in who can't offer anything.
"You think back to Denis Suarez who came to the club and physically he just wasn't ready and then he picked up injuries.
"It was a bit of an embarrassment in the end, so hopefully they will do their homework on Odegaard."
Suarez moved to the Emirates Stadium from Barcelona in January 2019 on a short-term loan deal.
But injuries limited the Spaniard to just six appearances all season and he returned to Catalonia without leaving an impact.
Smith continued: "He's [Odegaard] a young player that went to Real Madrid, and so much is expected of him, and as so often happens it doesn't quite materialise like that.
"But they've been looking for more creativity. [Emile] Smith Rowe has provided that. They were linked to Christian Eriksen as well the other day. So it's that kind of player that can make the difference against a deep-lying defence that's defending in numbers.
"I wouldn't be expecting him to start many games, somebody that would just dip in and out perhaps.
"But Arsenal have almost got one hand tied behind their back because financially they can't throw money at it so they've got to be fairly creative in getting these loans in."
Martin Odegaard has chosen to join Arsenal on loan rather than Real Sociedad. [as] pic.twitter.com/R6JeUeiaZd- AFTV (@AFTVMedia) January 22, 2021
Arsenal currently have another Real Madrid midfielder on the books, with Dani Ceballos in his second loan stint.
"Ceballos has been brought in from Real Madrid and they've got that relationship," the 58-year-old added.
"Ceballos has done well during his time at the Emirates I think so hopefully Odegaard could come and he's got a point to prove and he could add something to what they've got."
Arsenal will be hoping Odegaard hits the ground running, having been eliminated from the FA Cup on Saturday afternoon at the hands of Southampton.
Featured Image Credit: PA Images
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