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The perennial German champions are determined to sign land Mane, who was such a huge figure for Liverpool last season, and an initial offer of £25m was rejected at the weekend.
Bayern Munich have doubled down by again telling Robert Lewandowski that he cannot leave before his contract expires next year.
Sportsmail reported that Liverpool dismissed Bayern's bid of £21m plus a further £4.6m in add-ons which included if the Germans won the Champions League. Liverpool want £42.5m.
Robert Lewandowski has confirmed he is only interested in joining Barcelona.
The club's top executives have maintained that they are planning on holding on to the league's top scorer, but Lewandowski has been staging a rebellion of sorts.