"Neither the player has told us that he wants to change, nor is there an offer from Liverpool", Rangnick told Sky.
He was taken off after fouling Alessandro Schoepf on 54 minutes - his fifth booking this season which means he is suspended for next Saturday's game against Freiburg. He might have got another for a foul on Max Meyer before Leipzig coach Ralph Hasenhuettl made a decision to take him off with just over 20 minutes remaining.
The Germany striker was being held by Hertha defender Niklas Stark and appealed for a penalty when they both fell over, only for the ball to come off Stark and loop over his own goalkeeper.
Stuttgart climbed away from the relegation zone and was just four points behind Hertha in mid-table.
Recent reports suggested that Liverpool were looking into the prospect of bringing the move forward by five months, though, as they are keen to bolster their midfield ranks for the business end of the current season.
Hertha had 10 efforts on goal compared to the home side's seven. He's only scored a couple of goals, he seems a little bit distant.
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.
Hoffenheim had earlier missed their chance to move back to the top three after drawing 1-1 at lowly Werder Bremen.
At least 773 detained in protests in Tunisia
The United Nations expressed concern at the number of arrests, and urged the authorities to ensure people can protest peacefully. The interior ministry said the aim of the perpetrators was to "sow chaos like that recorded in some parts of the country".