According to the Daily Mail, the Hammers are set to step up their pursuit of the 23-year old defender who impressed on loan at Upton Park last season.
It is believed that Slaven Bilic wants to bring in a new full-back and will go after Jenkinson for another season-long loan after he made 36 appearances under Sam Allardyce last term.
Jenkinson is down the pecking order at the Emirates Stadium behind Mathieu Debuchy, Hector Bellerin and Calum Chambers and Arsene Wenger is likely to send him away for regular game time.
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