The Germany coach has distanced himself from the rumours linking him to the job at the Santiago Bernabeu, pointing out that he has a contract with die Mannschaft until 2014
The trainer made clear that he has two more years on his contract and is intent on guiding die Mannschaft to glory at the 2014 World Cup in Brazil.
When asked whether there is some truth in the rumours suggesting he could replace the 'Special One' at los Blancos, Low was adamant that such a development is not an option at the moment.
"At some point, perhaps I may return to coaching at club level. Right now is not the time. I am incredibly proud to be national team coach, and this has given me great joy during all these years," the 52-year-old told Sport 1.
"I do not concern myself [with the rumours]. This is just speculation, Jose Mourinho has a contract until 2016. I have a contract with the DFB until 2014," Low is also quoted as saying by ZDF.
"The best thing I could hope for is to become world champion with Germany before I leave. I have never said I will call it quits for sure after World Cup 2014.
"I have not thought about it or talked with anyone on this topic. We must first secure qualification. Then I will hold talks with everyone involved."
Low served as Jurgen Klinsmann's assistant for two years before taking the helm of the national team after the 2006 World Cup.