The Spaniard has long been an admirer of the winger, and could go head-to-head with his bitter rival Sir Alex Ferguson over the player's signature.
The Dutch international is believed to be valued by his club at around £18 million. Manchester United, still yet to spend much of the £80 million received from Real for Cristiano Ronaldo, would have no problem meeting that valuation if they decided it was a fair price.
In contrast, Liverpool might struggle to come up with the money required before the transfer window shuts in seven days' time. Club owners Tom Hicks and George Gillett have spent the summer restructuring the club's debts, with the consequence that Benitez has been told their will be no more money to spend.