The 23-year-old Egypt international won three consecutive Super League titles with Basle and also played in European competition.
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Elneny is expected to offer some much-needed cover in midfield, with the likes of Jack Wilshere and Santi Cazorla still recovering from injury.
Arsenal added the deal was “subject to the completion of regulatory processes”, but hope Elneny could feature in the squad at Stoke on Sunday.
