US Davis Cup debutant Sam Querrey will face world number one Rafael Nadal in the opening rubber of the semi-final on Friday.
Andy Roddick will then take on world number five David Ferrer in Madrid's Las Ventas bullring.
Saturday's doubles will pitch Madrid-born Fernando Verdasco and Feliciano Lopez against Mike Bryan and replacement partner Mardy Fish, after the withdrawal of Bryan's twin brother Bob.
Roddick, ranked eighth in the world, will play Nadal in the first of the reverse singles on Sunday, followed by Querrey against Ferrer.
The winning team will play Argentina or Russia in the final.
