The 26-year-old was a target for Liverpool, Manchester City and Arsenal over the summer, as they tried to add his defensive expertise to their backlines.
Albiol had fallen out of favour with Jose Mourinho last year which had triggered the interest in his services.
However, the Spain international has no intention of turning his back on the illustrious team from the Spanish capital.
He told Spanish radio station Cadena Cope: "The season is like a long-distance race. I haven't had many minutes in the early part of the season but I'm working hard to force the manager to pick me.
"It's a difficult challenge but nobody has spoken to me about leaving the club. Football is all about the present and we must work hard.
"Between now and December, there are a lot of games and I have to make sure I improve with every game."