According to El Pais newspaper, the 19 include two who are under 18.
The players "came to Madrid by plane, then from Madrid they came to Barcelona and presented themselves at a police station to claim asylum," a Spanish police spokesperson told AFP.
The spokesperson added that the players' claims will be looked at on Thursday.
The Venezuelan National Baseball team will partake in the 2026 World Baseball Classic.
Unfortunately, the Spanish National Baseball team failed to qualify for the 2026 World Baseball Classic after losing to Chinese-Tappei 6-3 in the final game.
This marked back-to-back WBC qualifying finales Spain had lost, with the previous being to the Czech Republic.
Spain has experienced an increase in asylum claims from Venezuelans recently, with 63.5% of all demands in the country last year coming from the South American nation.
According to the United Nations, around eight million Venezuelans have fled the country since 2014 as the oil-rich economy imploded.
President Nicolas Maduro was sworn in earlier this year after claiming victory in an election on July 28th.
The United States and much of Latin America recognise opposition leader Edmundo Gonzalez Urrutia as the legitimate winner and have accused Maduro of staging a coup.
Venezuela was angered when Spain decided to give asylum to Gonzalez Urrutia in September and has accused Madrid of interfering in its affairs.