Rovers boss Mark Hughes is hopeful of completing the capture of the 25-year-old Paraguay striker over the weekend.
"We are very hopeful something may happen," said Hughes.
"Maybe in the next 24 hours a deal could be done.
"Santa Cruz is a young player, an international with a good reputation who is playing at a top European club. He is also a real threat in the air.
"We've had some positive indications from his people and hopefully something will happen.
"The good thing from our point of view is that his fitness levels are fine as he has been playing in the Copa America."