Rico, 24, is fast closing in on 150 appearances in all competitions for his Spanish club.
The stopper has revealed that big-spending Milan were interested in his services during the off-season, but Rico ultimately signed a new contract with Sevilla, which will run until the summer of 2021.
"Milan made me a very good offer, but Sevilla proposed a contract renewal," Rico told El Descuento de El Correo TV. "My head is here and my goal was always to continue."
Rico appeared in 35 of Sevilla's 38 La Liga matches during the 2016-17 campaign.