The report suggests that Leipzig may need to raise funds in order to comply with UEFA's Financial Fair Play rules and would be open to an early move if Liverpool pay between £13m- £17.5m.
Substitute Timo Werner scored one and set up another in the second half to cancel Naldo's equalizer as Leipzig moved a point above Schalke, and 13 behind leader Bayern Munich.
Rangnick told Sky Germany: "Neither the player has told us that he wants to change, nor is there an offer from Liverpool".
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.
Naldo levelled but Werner's entry turned the game around in favour of the hosts.
Earlier, Nigel de Jong made an unhappy return to the Bundesliga by conceding a first-half penalty as Mainz threw away the lead in a 3-2 defeat at Hanover.
GETTYLiverpool are prepared to wait until the summer to make a move for Thomas Lemar
The Reds had originally agreed to sign the midfielder at the end of the season for a figure that could eventually rise to £66million - depending on whether his club, RB Leipzig, qualify for the Champions League again. Referee Felix Brych allowed the goal to stand.
Will we see the Guinean touch down in the Premier League before the end of the month, though?
Fuellkrug netted the resulting penalty on 38 minutes, then hit the winning goal 15 minutes from time to complete his hat-trick. The 32-year-old Gomez's career began with Stuttgart youth sides before he helped the senior side win the Bundesliga in 2007.
The result leaves Stuttgart 12th, one place below Hertha, who hit the post through Austria global Valentino Lazaro in the first half.
Hoffenheim had earlier missed their chance to move back to the top three after drawing 1-1 at lowly Werder Bremen.
Augsburg defeated Hamburger SV 1-0 to leave the visitor stuck in the relegation zone.