Negotiations between the Spanish giants and Bale's current club Tottenham Hotspur over a potential world record transfer are believed to be in advanced stages, but the 24-year-old has not yet made the move to the Bernabeu.
Leading Madrid sports dailies Marca and As published online screen grabs from the shop section of Real's website, listing Bale as the team's number 11 alongside pictures of the strips for sale.
The gaff was soon spotted, though, and the shop section of the site was inaccessible later in the evening. Newspaper As said the online shop is operated by sports brand Adidas and not by the club itself.
Reports have been circulating for weeks that Bale will move to the nine-time European champions for a fee that could eclipse the €93.2 million ($123.6 million, £80 million) Madrid paid Manchester United for Cristiano Ronaldo in 2009.
Spanish media said Thursday that an announcement on Bale's signing may come within hours.
Last year Real listed Croatian Luka Modric as a player on their site before signing him, also from Spurs. The club blamed hackers for that mistake.