The 27-year-old midfielder was poised to join Bayern Munich on Monday but when that fell through Spurs moved just before the transfer window was due to close.
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"It was a last-minute job. When I came in this morning it wasn't something I was looking to do," Redknapp told Sky Sports News. "It's now just a question of the papers being lodged with the Premier League in time.
"We are playing Champions League football now and need a strong squad and I hope we have got the paperwork in on time, we will have to wait and see."
Redknapp said Spurs would pay around 8 million pounds for the midfielder who was in the Netherlands team beaten in this year's World Cup final by Spain.
"He's a great passer of the ball, I have watched him play for Holland, he is a top player and would be a big, big plus for us," Redknapp said.
Van der Vaart, who began his career at Ajax Amsterdam, joined Real from Hamburg in 2008 but dropped down the pecking order following Kaka's arrival from AC Milan last year.
New Real coach Jose Mourinho has signed teenager Sergio Canales and Germany's Mesut Ozil to further increase competition for places in the team.
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