The club's sports director Martin van Geel confirmed to Sportweek magazine that the Spanish champions have offered £16 million for the playmaker.
"Wesley told us that he is ready for the transfer," said Van Geel.
"We will now start a really nice fight with Real Madrid."
Real signed another Dutchman, Royston Drenthe, from Feyenoord on Thursday and their raid on the Amsterdam ArenA seems set to be successful.
"I am already thinking about life without him. If he goes that would be a great shame, really, a pity," said the coach, who has previously stated that the loss of Sneijder would be a huge blow to Ajax's Eredivisie chances.