The likes of Stoke, West Ham, Wigan and Southampton are all thought to have asked about the availability of the right-back on loan for the rest of the season.
However, Arsenal boss Arsene Wenger has rebuffed the offers for Jenkinson as he feels he could be needed for the remainder of the campaign.
Jenkinson started the season as first-choice due to an injury to Bacary Sagna and he impressed for the Gunners which resulted in him winning a call-up to the England squad.
The former Charlton man is highly-regarded at Emirates Stadium and he was rewarded with a new deal before Christmas.
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