The four-time Champions League winner, who has played 530 times for the club, has seen first-team opportunities dry up after injury issues and the form of Ferland Mendy.
Mendy has been a regular starter at left-back ahead of Marcelo, who had stated he was happy to be second choice.
The 33-year-old's current contract expires in June next year and it now appears he is open to the possibility of leaving the Spanish giants, possibly as soon as January.
El Nacional claim that the Brazil international has expressed his intentions to leave the Bernabeu to club president Florentino Perez.
And Marcelo wants to return to his former club Fluminense.
Perez has given the green light to Marcelo's wish if both parties can agree to a deal.
However, Real boss Carlo Ancelotti may want to keep the experienced full-back for the remainder of this season as they seek to win LaLiga for a 35th time.
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