It has seen Sampaoli, who is under contract until 2018, linked with a potential switch to Barca.
But Castro said the former Chile coach had been offered an extension to remain at the Estadio Ramon Sanchez Pizjuan.
"We want Sampaoli to remain here," he told Cadena SER on Monday. "His attacking game makes us happy. Sevilla have offered him another year."
Castro also confirmed Sampaoli's release clause was just €1.5 million, if another club wanted his services.
Last week, Sampaoli refused to rule out the possibility of taking charge of Barcelona, whose coach Luis Enrique is under enormous pressure.