Torres, 17, has been compared to current Real Madrid star Marco Asensio, another Spaniard who La Liga's big two battled for following his emergence at Mallorca.
Both clubs have been monitoring the teenager who is regarded as one of the best of Spain's next wave of talent over the last year and have now seen enough to convince them to jump into action.
Torres' current contract at the Mestalla runs until 2019 and includes a release clause of just €8m (£7m). According to Valencia-based newspaper Super Deporte, both Real Madrid and Barcelona are now ready to activate that clause, with Paris Saint-Germain and Juventus ready to do likewise.
AS meanwhile note the player they describe as a "right-footed version of Asensio" visited Real's training base in Valdebebas last year. Los Blancos have made noted efforts to change their transfer policy in recent years, looking to sign promising young players they can ease into the first-team with Asensio a prime example of its current success.
The club provided another demonstration of that during the summer, paying £38m to secure the services of 16-year-old Brazilian sensation Vinicius Jnr, another talent was also pursued by Barcelona. Real Madrid also recruited 19-year-old Theo Hernandez and 21-year-old Dani Ceballos to bolster their first-team squad.
Real and Barcelona are also vying for Marseille sensation Maxime Lopez, with Real manager Zinedine Zidane already a huge fan of his talents.
Torres meanwhile is regarded as the jewel of the Valencia academy having been at the club since the age of six, currently playing for the club's Mestalla side in the Segunda B, the third tier of Spanish football.
He was also part of the Spain squad that beat England in the Under-17 European Championship last May and has been included in the Under-17 World Cup in India next week.