The Paraguay international was strongly linked with a switch away from Ewood Park in the winter transfer window as Manchester City saw a number of bids knocked back by Rovers.
Manager Sam Allardyce was eager to retain Santa Cruz's services as he aims to ensure his side avoids relegation, but it appears the 27-year-old has his heart set on leaving the club in the summer.
"I felt I had needed to give back the club everything they gave me with more effort by playing another season," the former Olimpia and Bayern Munich forward told Fox Sports en Latinoamerica.
"Being threatened by relegation stopped me moving."
He continued: "My task at Blackburn is done, (the board) knew how I was thinking when I arrived to the club.
"I came here for continuity, to get up to pace again and I did pretty quickly. My intention was always to get in shape and then move to a big club.
"The transfer window put me in touch with people very interested in having me and of course I'm seduced by the idea of playing at very big club again.
"The Blackburn board are aware of that and accept it, but then we were in the relegation places and playing in the top flight is priceless for them. I understand that."