Valverde was born in the village of Viandar de la Vera, Province of Cáceres, Extremadura. After making his professional debut in Segunda División – Deportivo Alavés and Sestao Sport Club– he was transferred to RCD Español in 1986, making his La Liga debut on 31 August in a 1–1 away draw against Atlético Madrid. In a season that included a second stage he ended with 43 league appearances, scoring seven goals; in his final year, he was part of the squad that lost the 1988 UEFA Cup on penalties, to Bayer 04 Leverkusen.