Bild report that the German giants are ready to offer £34.6m for Mane, an improvement on their last offer which totaled around £30m.
However, the improved offer is still a long way from what the Reds want for the wanton striker after they put a £42million price tag on him.
With Liverpool agreeing the £85m deal with Benfica for Darwin Nunez, it seems inevitable that Mane will leave this summer and Bayern are looking to push through the best possible deal for them.
The 30-year-old has a year left on his contract at Anfield but has made it clear he wants to move, with the Reds happy to let him go if an offer is made.
Paris Saint-Germain and Real Madrid have also expressed interest in Mane, leaving Liverpool unwilling to accept a low-ball offer while other interested parties remain.
The Reds are believed to be confused by Bayern’s meager offers, especially as they are demanding the 33-year-old €50m (£43.3m) for Robert Lewandowski, who has also made it clear he wants to leave with one more year his contract.
Barcelona are leading the hunt for Lewandowski, although Paris Saint-Germain are also keen on the Pole, while Chelsea have also been linked with his performances.
Meanwhile, Nunez arrived at Liverpool on Tuesday with his move from Benfica imminent.
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MORE: Why Darwin Nunez turned down bigger offer from Manchester United to join Liverpool instead
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https://metro.co.uk/2022/06/14/bayern-munich-to-return-with-improved-sadio-mane-bid-16826583/ Bayern Munich return with improved Sadio Mane offer | Soccer