The Spanish giants reportedly sent scouts to watch the teenager in action for England’s under-19s during the international break.
Bellingham, who signed for Sunderland in the summer, starred for the Young Lions in a 0-0 draw against Montenegro last week.
His highlights from the match went viral on social media as fans hailed the 18-year-olds composure on the ball,
El Nacional report that Real Madrid scouts were present to watch Bellingham in action during the match.
Los Blancos president Florentino Perez is said to have asked chief scout Juni Calafat to send staff to the game.
The report adds that Perez is keen to bring the younger Bellingham brother to the Santiago Bernabeu.
20-year-old Jude moved to the Spanish capital in the summer from Borussia Dortmund.
His £115million arrival made him the most expensive British player of all-time and he has since been in impressive form for his new club.
He has scored 10 goals in 10 appearances across all competitions as well as providing three assists for his team-mates.
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The former Birmingham midfielder was also named the La Liga player of the month for August.
As for his younger sibling, Jobe completed a switch to Sunderland from Birmingham in July.
He is already a regular for the Black Cats, appearing in all 11 of their matches in the Championship, scoring twice and adding an assist.