The Daily Mail says Saints boss Ronald Koeman is interested in the 25-year-old as a potential replacement for Dejan Lovren.
And the south-coast club have been made aware that Leverkusen will consider both permanent and loan moves for Wollscheid before the transfer window closes.
Wollscheid said recently: "Outside of Germany, the main interest seems to be coming from the English Premier League, but I don't know yet. We will have to wait and see."
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