Reports earlier this month suggested Nadal had reversed his decision not to play in the 2012 competition.
However, he was not in the four-man team named by captain Alex Corretja on Tuesday.
David Ferrer was though. Another member of the team which won last year's final, Ferrer had also said he would not play in 2012 but he has gone back on that decision.
Nicolas Almagro, Marcel Granollers and Marc Lopez make up the team which will entertain Austria in Castellon.
The visitors will be led by Jurgen Melzer but face a huge task on the clay - Spain have won their last 24 ties on the surface.
World number one Novak Djokovic has also opted out of Serbia's trip to the Czech Republic.
In his absence, Janko Tipsarevic and Viktor Troicki are likely to play singles for the 2010 winners. Dusan Lajovic and Nenad Zimonjic complete the Serbian team.
The Czechs name their regular duo of Tomas Berdych and Radek Stepanek, plus Lukas Rosol and Frantisek Cermak.
As ever, France name a strong side for their home tie against the USA, one which will take place on clay at the Monte Carlo Country Club.
Jo-Wilfried Tsonga and Gael Monfils appear likely to play singles, with Michael Llodra and Julien Benneteau also included, leaving no place for Richard Gasquet and Gilles Simon.
The Americans reunite twins Mike and Bob Bryan in their side for the claycourt tie. Bob missed the USA's first-round win due to his wife giving birth.
The Bryans will play doubles with Mardy Fish and John Isner chosen for the singles.
The other tie sees Croatia travel to Argentina.
The Croatians named Marin Cilic, despite their star man having only just returned to action on the ATP World Tour following injury, on Monday. Ivo Karlovic, Antonio Veic and Lovro Zovko make up their side.
The Argentines had already named their side. A full-strength line-up will be led by Juan Martin Del Potro in Buenos Aires.
The quarter-final ties take place from April 6-8.