The Spaniards tested the water last week with a bid reported to lie between six and seven million euros.

This was rejected out of hand by the northern Germany club, and a follow-up bid has been lodged since the sides met in London for the Emirates Cup this weekend.

Hamburg are still not tempted to sell, although Beiersdorfer has refused to call an end to one of this summer's longest transfer sagas.

"The offer was far from acceptable and was not in any way what we would have imagined," he told Germany's NDR television.

"Maybe something else will be coming next week."

Meanwhile, Hamburg coach Martin Jol laughed off Madrid's latest offer, claiming that the player would be worth 30 million euros on the current market.

Only the fact he can leave for just 1.5 million euros next July means Hamburg would consider releasing him at a cut-price fee, but they still expect to receive half his valuation.

"I have never seen a better player than Rafael," said Jol.

"He is the best number 10 in Europe and I would estimate him to be worth 30 million euros.

"What Real have now offered is a joke. Quite frankly, I would be very disappointed if the club let Rafael go for that sum, which is below that which we have discussed and agreed with him."

Hamburg are now holding out for the full 15 million euros which could still come their way before the transfer deadline on August 31, should Real fail in their bid to sign Cristiano Ronaldo from Manchester United.