Keita is due to leave Leipzig for Liverpool at the end of the season, but media reports suggest the English club is interested in bringing forward the transfer.
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.
Signing Keita early would be the ideal way to replace Coutinho with the Guinean described as the flawless fit for the way that Klopp plays.
The box-to-box midfielder has already agreed a £48million move to Liverpool with a clause which states the player won't be registered until the end of the current season.
After Leipzig's Jean-Kevin Augustin had a penalty saved by Schalke goalkeeper Ralf Fahrmann, Keita struck by rifling a shot home off his right boot on 41 minutes.
Naldo levelled but Werner's entry turned the game around in favour of the hosts.
Portugal midfielder Bruma then slammed home a third goal two minutes later as Schalke suffered a first loss in 13 games, a run stretching back to September.
Leipzig are already out of the Champions League and the midfielder would be ineligible to play in Europe were he to move to Liverpool in January.
Will we see the Guinean touch down in the Premier League before the end of the month, though?
His new club claimed early goals by Japan striker Yoshinori Muto and Alexander Hack. The 32-year-old Gomez's career began with Stuttgart youth sides before he helped the senior side win the Bundesliga in 2007.
The defeat leaves Mainz 15th in the table, just a point above the bottom three, while Hanover climb to 10th.
The result leaves Stuttgart 12th, one place below Hertha, who hit the post through Austria worldwide Valentino Lazaro in the first half.
Eintracht Frankfurt and Werder Bremen were held to 1-1 draws at home by Freiburg and Hoffenheim, respectively.
Augsburg defeated Hamburger SV 1-0 to leave the visitor stuck in the relegation zone.