BBC Sport says Arsenal are prepared to consider parting with the teenage England left-back at the end of the season - but at a starting price in the region of £40-50m.
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Manchester United are keen, seeing Lewis-Skelly as an eventual successor for Luke Shaw.
And contact has been established with the youngster's camp about a move to the Northwest this summer.
Lewis-Skelly has made 28 appearances across all competitions this season, but has started just once in the Premier League,