The striker spent last season on loan at Racing Santander, he drew attention to himself by scoring 13 goals in 19 appearances for the La Liga outfit.
Sam Allardyce was one of the managers alerted to the player who has been the subject of much speculation over the past few weeks
"I have rejected all the offers because my desire is to stay with Valencia the next season," Zigic told Las Provincias.
"I am very happy to return to the team and I am prepared to demonstrate to the coach (Unai Emery) that I should be in the team. This is my challenge now.
"My agent had many proposals from Spain and Europe but my decision was always clear. To stay at Valencia. I have not personally spoken with the coach but Valencia know my intentions and I will not change my mind."