According to the Daily Mail, agents have actively offered the 19-year-old to United.
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The England left-back is unhappy with his lack of playing time at the Gunners. After Lewis-Skelly was a regular starter last season, his development has stalled this term.
Behind Riccardo Calafiori (23) and Piero Hincapié (24), the England international has struggled to get off the bench.
United are seeking a new left-back addition to compete with Luke Shaw (31) for next season and Lewis-Skelly is now being discussed inside Carrington.