The Daily Mail says Bayern Munich have seen an offer of €67.5m for Colombia international Diaz rejected by Liverpool this week.
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The Reds are demanding €100m to sell their experienced winger in the coming weeks.
Diaz is also attracting interest from Barcelona and has reportedly informed Liverpool he wishes to leave Anfield this summer.
The 28 year-old's deal with Liverpool is now inside it's final two years, running to 2027.