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Both players have just a year left on their contracts and West Ham will undoubtedly be planning for the future.
Lopetegui is also lacking decent cover for Emerson Palmieri on the left-hand side and one of their targets would solve their issues at full-back.
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With West Ham on the lookout for a new full-back, Kyle Walker-Peters would tick plenty of boxes for Lopetegui.
The Tottenham academy product is able to operate on both sides and despite spending a season in the Championship with Southampton last time out, he boasts considerable experience in the Premier League.