The 26-year-old - who has made 36 league appearances for the Bernabeu outfit since arriving from Hamburg - seemed surplus to requirements this summer, following the club's £200 million spending spree on Kaka, Cristiano Ronaldo, Xabi Alonso, Karim Benzema, Alvaro Arbeloa and Raul Albiol.
A host of sides, including Liverpool, Arsenal, Chelsea, Spurs, Everton, Aston Villa, Inter Milan and Lazio, were linked with moves for the midfielder.
However, he was eventually spared the chop, after Arjen Robben and Wesley Sneijder were sold to Bayern Munich and Inter respectively to help balance the Madridistas' books.
Unsurprisingly, Van der Vaart has struggled for minutes under Manuel Pellegrini in 2009/10, making just three la Liga appearances.
With Holland coach Bert van Marwijk having already warned the midfielder that he may miss out on next summer's World Cup finals should he not play regularly this season, the playmaker is thought to be open to a New Year switch away from Spain.
And, according to The Sunday Times, Real will offer Chelsea Van der Vaart's services in January, with the Dutchman eligible to play for a new side in the Champions League knockout stages, having not been selected in any of Real's opening three group stage games.
Nevertheless, the player has insisted that he remains happy to stay in the Spanish capital and fight for his place.
"I wasn't fit [at the start of the season] and there was a lot going on in my head. I didn't do well in training," he told the club's official website.
"Now I am very happy and I want to prove I can be important. 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 in the team."
