Keita has scored five goals for Leipzig, and assisted another, in all competitions so far this season, but it is his disciplinary record side has Rolfes anxious.
Michael Edwards, Liverpool's sporting director, will hold discussions with his opposite number Ralf Rangnick about the possibility of bringing forward Keita's arrival.
The Guinean worldwide was due to arrive in Liverpool this summer in a transfer deal of between £58 and £68M (dependent on Leipzig's performance this season).
Otherwise, the danger for Liverpool is that after losing Coutinho, they will merely allow Mohamed Salah or Sadio Mane to move to the front of the queue for the next big-money move out of Anfield. "There are contracts which say that he will be a Liverpool employee from 1 July onwards".
So if they miss out, who else could they sign?
GETTYPhilippe Coutinho completed his £142m transfer to Barcelona earlier this month
Thomas Lemar, Riyad Mahrez, Christian Pulisic and even Antoine Griezmann - take that one with a pinch of salt - have been linked with the club in recent days, going to show how far they have come since Klopp arrived on these shores.
Other rumoured signings include Arsenal duo Alexis Sanchez andMesut Ozil, both of whom are now unsettled at the North London club, and Schalke midfielder Leon Goretzka. Coutinho was best man at Firmino's wedding last summer.
Firmino, Coutinho, Sadio Mane and Mohamed Salah had formed a part of Liverpool's vaunted "Fab Four" this season as the Reds terrorised Premier League defences but with Coutinho's departure, the quartet has split to leave Reds fans anxious about the strength of Jurgen Klopp's squad. His very future as Liverpool boss may depend on his next moves in the transfer market.