The London Evening Standard says the former Liverpool midfielderâ€™s current deal at the Bernabeu expires in the summer and he will be able to sign a pre-contract with a non-Spanish club in January.
The 31-year-old spent three years under Mourinho at Madrid and sources in Spain suggest he will be offered a three-year contract to move to west London.
Speaking in June following Mourinho's departure from Madrid, Alonso commented: "He's someone who can touch a chord and knows how to perfectly transmit messages in the dressing room. He is a good communicator.
"He knows how and when to make quick decisions which can change the outcome of a game."
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