The 17-year-old is yet to make his first-team debut for Valladolid but has caught the eye at youth level and was on the scoresheet against Atletico Madrid's youth side on Saturday.
According to Sport, the midfielder's displays have captured the attention of Barca, who have been impressed by his energy and goalscoring exploits from a deeper position.
The report claims that the financial impact of the coronavirus outbreak could lead to Ronald Koeman's side looking to youngsters for inspiration, with Pedri providing to be a huge success for the first team this season.
San Jose scored 21 goals at youth level last term, and Barca are thought to be one of a number of clubs monitoring his progress.
The Catalan giants are also believed to be close to completing deals for Manchester City duo Sergio Aguero and Eric Garcia, who are both available on free transfers this summer.
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