The Spanish giants have been watching Fernandes closely at the World Cup with Portugal.
The United attacking midfielder has managed two assists and two goals in his team's first two matches.
Per Record, Fernandes may even be lining up a move to Real in the near future.
While he did sign a new United deal late last season, Fernandes may find the lure of Real too hard to resist.
The source adds that Real may tempt Fernandes with Champions League football as well.