Odegaard has been regarded as one of the hottest prospects in world football ever since Real paid £2.3m for his signature in January 2015, but much of his development is being spent out on loan.
Since January, the 18-year-old has been with Heerenveen where he has made 23 appearances in all competitions, but it appears that Valencia are keen to ensure that the Norwegian experiences La Liga action before competing for a place at the Bernabeu.
According to Super Deporte, Valencia intend to propose a two-year loan deal to Real, meaning that they would possess the player's services from 19 years of age to 21.
Real are unlikely to use Odegaard in their senior setup for a number of years, although there is an acceptance that the Champions League holders will not want to sell the teenager on a permanent basis.
Odegaard is tied to Heerenveen until the end of the current campaign.