Liverpool have already agreed to pay the Guinean's £48m release clause which can not be triggered until next summer, with the Reds also agreeing an additional transfer fee to agree to the deal early, with the the midfielder due to move to Anfield in July.
But now Bild claim that Leipzig's attitude has changed and they are open to letting the 22-year-old leave now, but only if they receive a sum between £13m and £17.5m.
What's more, RB Leipzig are reportedly seeking for a cash injection in order to avoid a breach of UEFA's Financial Fair Play rules.
Leipzig are already out of the Champions League and Keita would be ineligible to play in Europe were he to move to Liverpool in January. Last week CEO Oliver Mintzlaff rejected talk that Keita was pushing for an early move to Liverpool.
"Neither Naby nor his agent have made the request to leave the club in the winter", he said.
The Reds had officially confirmed they would be signing the Guinean midfield dynamo at the start of next summer's transfer window before the current season began, in a deal believed to be worth around £48m.
The Guinea global will be unable to play in the Champions League but will give added squad depth in the Premier League as Liverpool battle for a place in the top four.