The move has already set Liverpool back £48 million after the Reds triggered Keita's release clause, last summer and to land him six months early could cost somewhere in the region of another £35 million.
The Reds had originally agreed to sign the midfielder at the end of the season for a figure that could eventually rise to £66million - depending on whether his club, RB Leipzig, qualify for the Champions League again.
Only last week, Leipzig CEO Oliver Mintzlaff played down claims Keita could leave.
"When we had this conversation around Coutinho, I said the same. We don't have a reason to sell before the summer".
Keita, though, has been criticised recently for his performances, with the Bild report stating he is now being distanced by his Leipzig team-mates.
He was taken off after fouling Alessandro Schoepf on 54 minutes - his fifth booking this season, which means he is suspended for next Saturday's game against Freiburg.
For their part Leipzig are insisting that nothing has altered, with head coach Ralph Hasenhuttl commenting: "The situation hasn't changed".
According to the, Liverpool are willing to listen to offers around the £30m mark for the striker, who has scored three goals in 14 appearances so far this season. Combining the two strands of information together appears to give the reports some legitimacy at least, though nothing has yet been confirmed by either club.