A recent report claimed the Catalans had attempted to sign the Frenchman, but they have denied that they are keen on the defender
TV3 claimed earlier this week the Liga champions were ready to trigger the centre-back's €30 million release clause and had already approached Varane's agent to discuss a potential transfer, only to be turned down by the France international.
However, Freixa has stressed there is no truth in the rumours linking the 20-year-old with a move to Barcelona.
"No, Barcelona have not attempted to sign Varane," the Barca spokesperson told reporters.
Varane joined Madrid from Lens in the summer of 2011 and has since developed into an integral part of the Santiago Bernabeu side's first team. He has a contract with los Blancos until June 2017.
Barcelona are keen to add some fresh blood to their defence this summer and have also been linked with players such as Mats Hummels,Thiago Silva and David Luiz in recent months.