Xabi's current deal expires in June.
The Daily Star Sunday says the Premier League rivals are gearing up for a transfer scrap next summer over the signature of the ex-Liverpool midfielder.
Alonso, 32, is out of contract at the end of this season and has so far failed to agree a new deal at the Bernabeu.
As long as that uncertainty persists, both the Gunners and United will stay hot on the heels of the World Cup and European Championship winner.
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