Both clubs had the centre-back watched in last weekend’s game against Racing Santander with a view of making a summer bid for the player’s services.
Real Madrid director of recruitment Paco de Gracia was present, just like Barcelona scout Emilio Gutierrez.
Sporting have recently renewed Borja’s contract and have no intention to sell, but this could change in case a big money offer arrives in the summer.
Borja Lopez, 19, has come through the youth ranks at Sporting Gijon and started this season in club’s B squad.
He was promoted to the senior squad in October and has since made 10 appearances for los Rojiblancos in Segunda, earning no less than 8 yellow cards in the process.
Borja Lopez is a member of Spain Under-19 squad at the moment, but he has also represented la Furia Roja at Under-18 and Under-20 level.