The Dutch international has made 32 league appearances - netting five times - since joining the Madridistas last summer.
However, following the expensive acquisitions of Kaka, Cristiano Ronaldo, Karim Benzema and Xabi Alonso, Real are open to offers for Dutch quintet Van der Vaart, Wesley Sneijder, Arjen Robben, Roysten Drenthe and Ruud van Nistelrooy, while Klaas-Jan Huntleaar has already departed for AC Milan.
A move appears inevitable for the 26-year-old, after he was not handed a squad number ahead of the new season.
Hamburg, Ajax, Inter Milan, Chelsea, Tottenham Hotspur, Aston Villa and Arsenal have already been linked with the midfielder, who has been capped 69 times by his country.
And, according to The Times, Anfield chief Rafael Benitez is the latest to express an interest in the Dutchman, with the Spaniard believed to be weighing up a £6 million move.
Van der Vaart recently revealed that he is keen to complete a switch to the Premier League, should the opportunity arise, saying:
“I really want to come to England.
“I want to go to the Premier League and I know where I want to play.”
Liverpool are also expected to sign Greek centre-back Sotirios Kyrgiakos in a deal believed to be in the region of £1.5 million.
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