Real have failed to score in the past five games and president Florentino Perez is seeking an experienced striker signing to make an instant impact.
Cadena Cope says Ibrahimovic is on the radar, knowing he will be available in January for loan.
The Swede, 37, has scored 22 goals in 26 games so far this MLS season.
For his part, Ibrahimovic hasn't shut the door on returning to Europe in the New Year for a short playing stint.
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