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 Rangnick says neither Keita - who scored in Leipzig's 3-1 defeat of Schalke on Saturday - nor Liverpool have made any such requests.
The fee Liverpool will pay for Keita is dependent on Leipzig's final league position - £67m if they qualify for the Champions League and £57m should they miss out.
"Neither the player has told us that he wants to change, nor is there an offer from Liverpool", Rangnick told Sky Deutschland.
Schalke goalkeeper Ralf Faehrmann saved a penalty from Jean-Kevin Augustin but there was little he could do to stop Keita's effort from distance after it took a decisive deflection from defender Naldo about five minutes before the break.
Naldo levelled but Werner's entry turned the game around in favour of the hosts.
European's elite competition could be a vital factor in any possible deal though as RB Leipzig are fighting for qualification into the Champions League and may want to hold on to such a player.
However, after Hanover striker Niclas Fuellkrug made it 2-1 with a header towards the end of the first half, De Jong brought down midfielder Felix Klaus in the area and the referee pointed to the spot.
Stuttgart climbed away from the relegation zone and was just four points behind Hertha in mid-table. He will play with us until the end of the season.
While the German worldwide was appealing for a penalty, the ball looped off Stark's boot and into the net for the winning own goal on 78 minutes.
Elsewhere, Augsburg climbed to seventh with a 1-0 win over strugglers Hamburg thanks to a winning header by South Korea worldwide Koo Ja-Cheol.
Augsburg defeated Hamburger SV 1-0 to leave the visitor stuck in the relegation zone.