The Norwegian forward has been on loan at Vitesse Arnhem this season, so Ajax have had ample oppurtunity to watch him in the Eredevisie.
Now they could be tempted to make an offer for the 20-year-old amid reports that Real Madrid will sell for a cut price, according to De Telegraaf.
Ajax require financial savviness to continue competing at the top and prefer cheaper, good-value deals, or to promote from within.
But their director of football Marc Overmars is leaning towards a move to Odegaard if, as is reported, Real Madrid leave some negotiating wiggle room.
The report claims that Madrid may well do a special deal with Ajax which could include the insertion of clauses.
Odegaard has eight goals and nine assists this season and could be ripe for an Ajax side widely expecting to lose a number of their Champions League heroes this summer.
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