Manager Rafa Benitez is in the market for a right-back to take over from veteran captain Seamus Coleman.
But his hands are tied by a lack of cash and he is now exploring the possibility of signing Chambers for a nominal fee.
The 26-year-old former England international is currently in the final few months of his Arsenal contract and the club have yet to take up the option to extend his deal by a further year.
Press speculation states there is a chance that Arsenal could sell him in January for a fee in the region of £5million rather than lose him as a free agent in the summer.
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