The 22-year-old came off in the second half as Leipzig ran out 3-1 winners and move into second in the Bundesliga.
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.
Rangnick told Sky Germany: "Neither the player has told us that he wants to change, nor is there an offer from Liverpool".
Liverpool reached an agreement with RB Leipzig last summer for the Guinean midfielder to transfer to the English team next summer in exchange for €75 million ($91.5 million).
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I would like to hope he will be closer to one month rather than months". "He has done well very recently for us". I said when I came here that the only thing that matters to me is where we are on the final day in May.
Keita was booked in the second half, his fifth yellow card of the season ensuring he'll be suspended for the following game.
The defensive midfielder played for the Netherlands in the 2010 World Cup final defeat by Spain and won the 2012 Premier League title with Manchester City. He might have got another for a foul on Max Meyer before Leipzig coach Ralph Hasenhuettl chose to take him off with just over 20 minutes remaining.
It shows clearly that he intends to keep his young star until the end of the season.
Hoffenheim had earlier missed their chance to move back to the top three after drawing 1-1 at lowly Werder Bremen.
Eintracht Frankfurt and Freiburg also drew 1-1 while Augsburg moved on to 27 points with a 1-0 victory over Hamburg SV.