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Negotiations between the Spanish giants and Bale's current club Tottenham Hotspur over a potential record move 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 £80 million Madrid paid Manchester United for Cristiano Ronaldo in 2009.
Spanish media said on Thursday 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.
Spurs boss Andre Villas-Boas refused again to be drawn into speculation over Bale's future.
"I am not able to comment on anything, that has been my tone since the start of the season and I will not change that," said Villas-Boas after his team's 5-0 win over Dinamo Tbilisi in the Europa League on Thursday.
