The 17 year-old, known as 'Chuky', has never tasted first team football with Valladolid, but enjoys a growing reputation inside Spanish football.
Sport via Le 10 Sport says Barca's scouts have been impressed and are recommending they move for the youngster this summer.
An initial plan is to sign San Jose from Valladolid before loaning him back to his formative club for next season.
The youngster is being likened to Barca superkid Pedri, who signed for the Catalans in 2019, but spent that season on-loan with his former club Las Palmas before joining the Blaugrana this term.
Barca have similar plans for Chuky, who plays in the same fashion as Spain international Pedri.
Chuky has quietly gone about his football this season, though Barca's interest being made public is expected to flush out more suitors. As such, Barca are eager to close a deal quickly before rivals have time to act.
- updated May 18