Keita secured a move to Liverpool back in August, but the complicated transfer is not due to be complete until the end of the campaign.
Liverpool reportedly triggered a £48 million release clause which is due to become active on July 1 2018, while they are 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, they are by no means guaranteed a Champions League spot, although they occupy the final qualification spot ahead of Sunday'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 says neither Keita — who scored in Leipzig's 3-1 defeat of Schalke on Saturday — 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 told Sky Deutschland.
"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."