The right-winger has risen through the youth ranks at Madrid since joining from Penya Arrabal's academy in 2016, and he made four La Liga appearances under Zinedine Zidane last season.
Park started in two victories versus Getafe and Granada - bagging an assist against the latter as a right-back - but Los Blancos are thought to be keen to send him out on loan for the new campaign.
According to Italian journalist Gianluca Di Marzio, Park's performances have caught the eye of Torino, and Real Madrid would be happy to sanction a temporary move in order for the 20-year-old to gain some valuable experience.
Park has accumulated four goals and three assists for Real Madrid Castilla during his time in the Spanish capital, and he was on the bench for Los Blancos' 0-0 draw with Liverpool during the second leg of their Champions League quarter-final tie last season.
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