The 27-year-old has been heavily linked with a move away from his Catalan employers, with Real Madrid, Barcelona and Manchester United among those reported to be keen on acquiring his services.
Casilla is, however, happy in his current surroundings and has no intention of pushing for a move.
Instead, he hopes to extend his stay with Espanyol, with his representatives in discussions regarding fresh terms.
Casilla, who spent time in Real's academy system during his younger days, told Agency EFE: "I am not concerned about the rumours regarding my future.
"I am pleased to hear my name mentioned in the press alongside Barcelona, Real Madrid and big English clubs, but my intention is to remain at Espanyol.
"I am in negotiations with the club over a new deal and I hope to reach an agreement soon.
"I don't believe that the club are planning to sell me if they want to renew my contract, that would be a lack of respect.
"I don't have a set date for the signing of the documents, that is a matter for my agent, but I am calm."