TV3 report that the Catalans, as well as Manchester United, were interested in the French defender, who starred for Real Madrid last season.
Varane has a 30 million buyout clause in his contract with Real Madrid.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.