The Dutchman was faced with a similar situation last summer, after Real brought in Kaka, Cristiano Ronaldo and Xabi Alonso, with Manchester United, Chelsea, Arsenal, Liverpool and Tottenham Hotspur all linked with moves for the midfielder.
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Ozil is not the only midfielder to be recruited by Real this summer, with Sami Khedira, Angel di Maria, Pedro Leon and Sergio Canales also joining Jose Mourinho's side.
But Van der Vaart, who scored in Madrid's 1-1 draw against Standard Liege on Tuesday, has insisted that he has no desire to leave for the likes of Old Trafford, Anfield or White Hart Lane.
"For me there is no problem with Ozil arriving. I will fight for my place. The club has not spoken to me, but Mourinho always tells us that we all have opportunities," he said.
"Being at Madrid is very hard, especially now, with the arrival of a player of great quality. But I want to stay and I know I'm going to play a lot."
He is expected to be more active in the transfer market should Spurs defeat Young Boys next week and reach the group phase of the Champions League, guaranteeing the club a cash windfall of up to £30 million.
