Born in Azul, Buenos Aires Province, Almeyda started playing professionally for local and national powerhouse Club Atlético River Plate, first as understudy to Leonardo Astrada then as a starter, helping the side to the 1996 Primera División title after his insertion in the starting XI, as well as that year's Copa Libertadores. Shortly after, he moved to Sevilla FC in Spain for a record fee for a player in the country of $9 million; he appeared regularly in his first and only season with the Andalusians, but suffered La Liga relegation.