The Mirror says David Moyes has tabled a £22million bid to take the Southampton left-back to champions United.
But the Londoners are determined not to let the 18-year-old move to Old Trafford, as they see him as the No1 successor to Ashley Cole.
United have been pushing to get a deal done in this winter window and there is a small chance of the deal happening before Friday's deadline if either club matches Southampton's valuation.
However, Shaw is willing to stay put - safe in the knowledge that Jose Mourinho's Blues will come back in for him in the summer.
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