Newly elected Real president Ramon Calderon claimed Predrag Mijatovic, his sporting director, has “been in touch” with Robben.
Peter Kenyon confirmed the club would be writing to world football’s governing body.
“We are aware of comments regarding Arjen made by Ramon Calderon, the new president of Real Madrid, since his successful election,” Kenyon said.
“The Arjen Robben situation could not be any clearer. There have been no meetings or conversations between the Real Madrid sporting director Predrag Mijatovic with any Chelsea officials, anyone mandated to act on Chelsea’s behalf or Roman Abramovich, about Arjen’s future. Any indication that a transfer is possible is completely untrue. We will not be entertaining any offers for Arjen, he is not for sale.
“Moreover, we note that Mr Calderon confirms that Real Madrid have spoken to Arjen. As a result of these various comments Chelsea will be writing to FIFA to ask them to investigate an illegal approach for our player.”