The former Chelsea defender comes off contract in June and his deal will not be renewed, reports transfer expert Fabizio Romano.
Alonso has played just seven games all season and started just four times between the championship and the Champions League, for a total of 299 minutes overall without goals or assists.
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The veteran's deal carries a 12 month option - but Barca will not trigger it.
For his part, Alonso also feels ready for 'a new adventure'.