According to Spanish publication Sport, Odegaard wants to return to Arsenal, telling his agents to negotiate a move back to the Gunners, after deciding that he should leave Real Madrid this summer.
The Norwegian spent the second half of last season on loan at the Emirates Stadium, impressing Mikel Arteta enough to encourage him to try and re-sign him this summer, with him wanting Odegaard on a permanent deal instead.
Arteta is currently targeting a move for an attacking midfielder, with Emile Smith Rowe the only playmaker in the senior squad apart from Joe Willock, who has been linked with a move out of the club.
While Odegaard looked set to stay at Real Madrid and try to break into Carlo Ancelotti's squad, Sport are claiming that Odegaard's poor performance in Real Madrid's defeat against Rangers in pre-season has changed the perspective in Spain.
The Spanish club is now considering selling the 22-year-old after his disappointing display, and with them in financial trouble, they are keen on generating some more funds this summer.
Odegaard has reportedly already told his agents to try and secure a permanent move elsewhere this summer, with him wanting to rejoin Arsenal as he wants to play in the Premier League and that Arteta's style of play suits him the most.
A report from football.london has also stated that while Odegaard would be ready to fight for his place in the Real Madrid squad, he is also open to moving to another club, while the Spanish club wants to offload him this summer.
Leicester City's James Maddison was seen as an alternative, yet the £60 million price-tag that the English midfielder has is set to prove a sticking point until several player sales are made.
While Arsenal have not made a formal approach for Maddison, it is understood that they have highlighted the possibility of signing the 24-year-old.
Odegaard played in 20 games in all competitions last season for Arsenal, and while he got just two goals and two assists, he did show promise of revitalising a poor Arsenal team that lacked creativity and cutting edge.