The 30-year-old striker never made a first-team appearance for the Bernabeu giants but he did star for Alcorcon when the Segunda Division B side humiliated Madrid in the Copa del Rey in 2009.
Killie are short of attacking options and Perez will feature for the SPL side in James Fowler's testimonial against Sheffield Wednesday on Wednesday night.
Shiels is hoping the forward, who also had a brief spell at Valladolid, can show his ability in the match.
Shiels told STV: "The chairman says there's no money which I have to accept. We've got a trial player in from Spain who is a support striker.
"He has got the attributes to play in our team but we have to see if that comes out (in the match) and see where the financial side is."