The teen has fully recovered from an ACL injury suffered last year, but has struggled to force his way into Real coach Xabi Alonsos plans this season.
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The Athletic is reporting Dortmund are tracking Martinez's situation and weighing up a January move for the 18 year-old.
Dortmund would seek an initial loan arrangement in January with an option to buy depending on various targets being met.
Martinez penned a new deal in September to 2029, but could be tempted away if offered better playing opportunites.