The Gunners have been linked with Norwich City’s Emiliano Buendia in recent months but appear set to miss out on his signature.
Aston Villa have agreed a club-record deal of £33 million with the Canaries, and the Argentine will undergo a medical after Tuesday.
While the Gunners had a ‘serious interest’ in Buendia, it is reported that Odegaard continues to remain the main transfer target.
Odegaard had a productive five-month loan spell with the Gunners with two goals and two assists from 20 appearances in all competitions.
Gunners technical director Edu is convinced that the playmaker can be re-signed in either a temporary or permanent deal this summer.
Odegaard made a slow start with the Gunners after his January move but adapted to the club’s style of play within a few weeks.
Aside from his goal contributions, the Norwegian impressed with the intelligent and precise passing, creating chances for his teammates to score.
Odegaard has two years remaining on his Los Blancos contract, and his future will be decided by Los Blancos’ new head coach Carlo Ancelotti.
Ancelotti likes to play with a number 10 in the line-up, and the 22-year-old could be offered the chance to establish himself with the Madrid giants.
However, the Gunners will hope to convince the £36 million-rated star to rejoin them with the assurance of a starting role, which may not be the case at Madrid.
The north London club re-signed Dani Ceballos for a second season on loan from Los Blancos last year, and they could propose a similar move for Odegaard.
If a temporary deal is to go through, Los Blancos may want Odegaard to sign a contract extension or the Gunners to include an obligatory buy clause.
Stats from Transfermarkt.com