Keita secured a move to Liverpool last August, but the complicated transfer is not due to be complete until the end of the campaign.
Liverpool reportedly triggered a £48million release clause which is due to become active on 1 July, while it is also said to have paid an extra £7m in order to secure the early transfer and loan him back for a year.
But with Liverpool one of four teams separated by just three points between second and fifth place in the Premier League, it is by no means guaranteed a UEFA Champions League spot, even if it does occupy the final qualification spot ahead of Monday's clash with Manchester City.
According to reports, that uncertainty over a top-four place coupled with the sale of Philippe Coutinho has urged Liverpool to consider bringing Keita to the club earlier than initially agreed by forking out a further £18m.
But Rangnick claimed neither Keita - who scored and starred in Leipzig's 3-1 defeat of Schalke - nor Liverpool have made any such requests.
"Neither the player has told us that he wants to change, nor is there an offer from Liverpool," Rangnick said. "He wants to leave us in the summer. He will play with us until the end of the season. There is nothing more to say."