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The Norwegian attacking midfielder has made 12 appearances for the Gunners and scored twice.
According to Spanish newspaper Marca, the Madrid loanee is still part of Los Blancos' long-term plans.
And Madrid reportedly have no desire to allow Odegaard to make a permanent switch to the Emirates in the summer.
Arsenal's loan for the Norway international does not include a buy option at the end of the season.
Marca claims that Madrid also 'do not contemplate' the idea of allowing Odegaard to leave the Santiago Bernabeu.
Arsenal hero Ian Wright has praised Odegaard since his arrival at the Gunners, saying the Premier League club could land him in the region of a £45m to £50m deal.
Speaking on Ringer FC's Wrighty's House, the 57-year-old pundit said: "His contract runs out in 2023 with Madrid, we're going through a spell where there's not a lot of money about, Madrid need money, if [Zinedine] Zidane stays there can you see him putting Odegaard in his team?
"You're thinking to yourself if he carries on playing like he is, because we're looking at [Luka] Modric and [Toni] Kroos and they're going to have to get replaced by someone at some stage now.
"Whether that's Odegaard or they might sell Odegaard to finance getting somebody else. When you look at him, this is serious business with Odegaard, this is a player we need, and I don't know how they're going to do that.
"For me, I think £45million to £50million, even though we're talking about someone who's been on loan to Holland, Spain and now here, he's played a handful of games but he looks so impressive.
"You have to pray, the Arsenal fan base have to put it out into the ether, the energy and the good vibes, to make it happen because he is needed."