United are in the market for two midfield additions ahead of the summer market.
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And La Gazzetta dello Sport says United have made contact with Thuram's camp about a move to England.
Liverpool are also interested, though it is only United which are currently in talks with the France international.
Thuram's future with Juve will be determined where they finish on the Serie A table at the end of the season. Should they miss Champions League qualification, Juve will need to make a major sale to balance the books.
Thuram is a likely candidate to be moved on, with the midfielder rated at €60-70m.