The reigning Primera Division champions are 11 points behind Barcelona in the table and on Wednesday suffered a 2-1 defeat to Celta Vigo in the first leg of their Copa del Rey fifth-round tie.
The loss to Celta was Madrid's sixth of the campaign in all competitions and means they have already lost more matches than they did in the whole of last season.
Reports in Spain suggested that the Portuguese will leave Los Blancos after an indifferent campaign to date, with Low one of the favourites to be his successor.
However Real president Florentino Perez moved this morning to quash rumours of Mourinho's departure describing him as "the best coach in the world", while Low insists his focus is firmly on Germany.
"I do not care about the rumours. This is just speculation, Jose Mourinho has a contract until 2016. I have a contract until 2014," he told German Television station Sport1.
Low has been in charge of Germany since replacing Jurgen Klinsmann in 2006 and has led his country to the Euro 2008 final, third place in the 2010 World Cup and the semi-final of Euro 2012.
"At some point, I may return to coaching at the club level. Now is not the time," he added.
"I am incredibly proud to be the national team coach, and this has given me joy over the years."