The 22-year-old has been strongly linked with a move to the Emirates Stadium in recent days, although Real Sociedad, who had the Norway international on loan last season, were also mentioned as potential suitors.
Arsenal were thought to be facing a battle to win the race for his signature, but Sociedad boss Imanol Alguacil has insisted that his side are not in the running for the attacker.
"I don't think that was an option at any time," Alguacil told reporters. "Clearly, with everything that he showed [here], what a good player he is, the team would grow even more, but at no time has there been any possibility that he would return here."
Odegaard scored seven goals and registered nine assists in 36 appearances for La Real last term before returning to the Bernabeu.
The Norwegian has found it difficult to make his mark for Zinedine Zidane's side this term, though, failing to score or register an assist in nine outings in all competitions. body check tags ::