The Eredivisie club are looking for creativity in midfield having failed to re-sign Mason Mount on loan from Chelsea - with the 19-year-old joining Derby County instead.
Odegaard has not been included in Madrid's first team squad for this season and therefore could well be sent out on another temporary deal; having spent the past 18 months at Heerenveen.
This means that both Aston Villa and Derby now have further competition in the race to sign the Norway international, with the Mirror reporting of the Championship duo's interest.
Los Blancos are keen for Odegaard to play regularly in a competitive environment having not developed as well as they would have wished since arriving at the Estadio Santiago Bernabeu back in 2015.
The teenager has played just twice for the first team, mainly operating in their Castilla reserve setup, but there are still high hopes for the Norwegian in the Spanish capital.
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