The Tottenham starlets have impressed in this season's NextGen series - the youth football equivalent of the Champions League - and the El Clasico duo are thought to be interested in bringing the pair to Spain.
Both Alex Pritchard and Shaquille Coulthirst have scored four goals in the competition - and are joint top scorers.
19-year-old Pritchard is out of contract at the end of the season, and Real Madrid are reportedly monitoring his situation at White Hart Lane.
The skilful playmaker was the shining light for Tottenham in both games against Barcelona, and found the net in Spurs' shock 4-1 win over the Catalans in Spain.
And Tito Vilanova's side are believed to be scouting 18-year-old Coulthirst, after the young forward hit three past the Barca youth team in the same game earlier this month.
Pritchard is something of a dead-ball specialist, and hit the target with a stunning free-kick against Wolsburg earlier on in the tournament. The 19-year-old typically operates in the centre of midfield, and was reportedly the subject of a bid from Premier League side Queens Park Rangers earlier this year.