La Gazzetta dello Sport says AC Milan and Juventus are exploring a winter move for the South Korea international, but are faced with one particular problem: Kim's salary.
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In Munich, Kim earns a double-digit million euro annually – too much for both Italian heavyweights.
The former Napoli defender would therefore have to accept a pay cut, otherwise a move is unlikely to materialize.
Bayern also would only approve the transfer if a suitable replacement is brought on board first.