The 26-year-old was recently rumoured to be a January target for Chelsea if they are able to have a FIFA transfer suspended, but van der Vaart wants to earn a second chance with Real.
- Premier League fixtures
- Premier League results
He told his club's official website: "I wasn't fit early in the campaign and there was a lot going on in my head. I didn't do well in training.
"Now I am very happy and I want to prove I can be important for the team and the coach has allowed me to play several minutes in the last few games.
"I have to take advantage of every chance I get to prove I can play here.
"I know it's hard, but I want to fight for Real Madrid and become important to the team."
Van der Vaart joined Real in the summer of 2008 from Hamburg, but has made just 20 starts for the Spanish giants and was told that he could move on before the current campaign got underway.