Madrid-born Morata moved to Juventus from Real in July 2014 for 20 million euros (£14.5 million).
Real president Florentino Perez hinted in September that the club might look into getting Morata back, Spanish media reported.
Morata has scored one goal in 13 appearances this season.
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Fifth-placed Juventus play Fiorentina in Serie A on Sunday.
(Reporting by Marianna Ciabach-Malinowska in Gdynia, editing by Ed Osmond)
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