There was a second bid worth up to 30 million dollars from the German club for Sadio.
The offer included add-ons, which the Reds believe are unrealistic, as well as the fact that he would have to lift the same number of Ballon d'Or trophies as everyone else.
The Reds value the 30-year-old who is about to enter the final year of his contract at around £43 million.
They have already turned down another offer from the German team, for an initial sum of around 25 million dollars.
When asked about his future last week, he said he would do what the people of his country wanted, and joked that he could sign for a French club.
A three-year deal for the winner of the African Cup of Nations is in the works for the German club.
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After the defeat to Real Madrid, he told Sky Sports News that he would make a decision on his future.
He said that he sees the comments on social media. Isn't it possible that between 60 to 70 percent of the people in the country want me to leave?
I will do what they ask of me. Soon, we will see. We'll see this together, so don't be rushed.