Bernabeu defender could be on his way to the Emirates, Stamford Bridge or Eastlands.
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Real Madrid defender Pepe has been told by the club to sign a new contract deal or he will be sold in the summer.
This has alerted Arsenal, Chelsea and Manchester City who are all in the market for a top-class centre-half.
The Portugal international is out of contract in June 2012 and has been in negotiations for months but Real Madrid are unwilling to meet his wage demands.
The latest offer is worth £3million, bringing him in line with Xabi Alonso and Gonzalo Higuain, and the La Liga giants are unlikely to offer any more.
Spanish newspaper Marca reveals that Real will sell the 28-year-old at the end of the season if he does not accept the offer.