Spanish outlet Don Balon, as quoted by the Daily Express, is reporting that the La Liga side are keen on a move to bring the full-back to the Bernabeu this summer.
The 27-year-old was a consistent performer for Chelsea FC last season despite the Blues’ stuttering form in the Premier League.
The west London side ended up in fifth place in the Premier League table as they missed out on qualification for next season’s Champions League.
Now, it is being claimed that Real Madrid are keen on a move to bring Alonso back to his native homeland this summer as they bid to strengthen their options at full-back.
According to the same story, Alonso could be on his way out of Chelsea FC this summer and Real Madrid are leading the chase for his signature.
The same article says that Chelsea FC are keen to sell the defender and that Real Madrid are confident of concluding a deal in the coming weeks.
Chelsea FC finished fifth but managed to beat Manchester United to win the FA Cup last season.
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