The 19-year-old Norwegian midfielder spent last season on loan at Heereveen in the Dutch Eredivisie and as part of his continued development is expected to make a move the the second tier of English football.
Odegaard was once touted as very hot property but failed to live up to expectations and break into Madrid’s first team.
However Los Blancos are keen to continue his process and English clubs have been alerted to the possibility of taking him on loan, report the Sunday Mirror.
Madrid hope that exposing the teenager to a tougher brand of football will improve his game.
Odegaard has expressed a desire to get regular minutes at his next club, whoever that might be.
“The important thing will be to go to a team where I can play,” he said at the end of last season.
Odegaard began his career in Norwegian football by breaking into Stromsgodset’s first team at the incredibly young age of 13-years-old.
Three years later Odegaard left Norway in a £3m move to the Bernabeu in 2015.
He initially played under Zinedine Zidane in Madrid’s reserve side, but the left-footed midfielder failed to reach the level expected to play at the Bernabeu.
Los Blancos were keen to continue his development and sent out the young Norwegian to Holland, in the hope he would gain valuable experience.
Odegaard’s 18-month loan spell at Heerenveen was productive as he made 40 Eredivisie appearances and scored three goals.
His time with the club was unfortunately cut short when he suffered a fractured metatarsal, five games before the end of the season.
The Championship loan window transfer deadline closes on August 31 and it’s expected many clubs will be looking to take on a player who could reach the potential he showed as a youngster playing in Drammen.