The Daily Mail says Abramovich will have to pay as much as £12million to bring Mourinho back to Chelsea.
The Real Madrid coach inserted a break clause in the four-year contract he signed at the Bernabeu last summer after he won La Liga.
Mourinho's contract runs until 2016, but Chelsea may have to pay Madrid up to a year of that to bring him back to Stamford Bridge.
Mourinho claimed he will be leaving the Spanish club after they were beaten in the Champions League semi-final for the third successive year.
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