Having been highly-rated for quite some time now, his performances in Russia have made plenty of teams sit up and notice.
According to 'Atresmedia', Real are one such club and they are believed to be keeping a close eye on his situation at Schalke.
The 22-year-old is a versatile midfielder who offers a bit of everything. At 6'3" the German offers physicality but he also possesses excellent technique, vision and an eye for a goal.
He scored 8 goals and created 6 more in 41 games for his club last season whilst he also managed to score 3 goals in 4 games at the Confederations Cup for Germany.
Goretzka and fellow German Timo Werner are considered to have been the stars of the tournament and have naturally both generated plenty of interest as a result.
Real are always on the lookout for young, talented players and no-one can argue that Goretzka is both of those.
It remains to be seen if the Spanish giants will make a move for the player at this time.