Van Dijk moved to Southampton from Celtic just under two years ago for £13.5m and the Scottish giants are understood to have included a 10% sell-clause in the contract.
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A source at St Mary's has told Sky Sports News HQ that, although the club has concluded a number of transfers with Liverpool in recent years, they feel the Reds have overstepped the mark in trying to convince Van Dijk to move.
The Premier League confirmed on Monday they will look into the matter, with a spokesman stating: "Southampton have raised some concerns and we are in turn raising them with Liverpool."