In a bid to replace Philippe Coutinho, who joined Barcelona earlier in the week, Liverpool are understood to want to push forward Keita’s arrival on Merseyside.
A £51million deal is already in place for the Guinea international to arrive in the summer.
But reports in Germany suggested Keita would play his last game for Leipzig against Schalke today.
Keita was named in the starting XI and he scored with a deflected strike in the first half.
The 22-year-old came off in the second half as Leipzig ran out 3-1 winners and move into second in the Bundesliga.
But after the match, Rangnick insisted Keita has not informed them of a desire to leave.
Rangnick told Sky Germany: “Neither the player has told us that he wants to change, nor is there an offer from Liverpool.”
Yesterday, Keita registered a company in the UK via Companies House amid claims the deal would be complete by Sunday and he would wave goodbye to Leipzig fans this weekend.
A company under the name ‘NK8 LIMITED’ has been registered on the Companies House website with two people listed as officers – Naby Deco Keita and Bjorn Alexander Bezemer.
Bundesliga journalist Chris Williams then tweeted: “Information from within Leipzig this evening that Naby Keita will become a Liverpool player on Sunday.”