The veteran defender is off contract at the end of the month.
Orta said: "He has demonstrated his performance, his leadership, everything he adds inside and outside. It would be very important in this time of so much change.
"Personally, I would be delighted (if he stayed).
"He knows Sevilla's intentions. We don't have a deadline. We have a pending conversation. Sergio deserves Sevilla to wait just as Sevilla deserves Sergio to wait."
On new coach Javi Garcia Pimienta, Orta added: "I am very excited and energetic because we have found a perfect coach for this moment of identity.
"And I also see him prepared for this challenge. Sevilla has to take another step. I have not stopped working for many years. I consider myself in my best moment as a sports director and it will be my best summer without a doubt. It is a club that I love.
"I am more excited than ever for Sevilla."