According to RMC, the Bundesliga outfit are keen on signing the midfielder on a free transfer at the end of the season as Jurgen Klopp looks to rebuild his squad following a dismal domestic campaign.
Liverpool, Newcastle and Everton have already made contact with Ayew, who is out of contract at the end of the season, while QPR saw a £1.5m bid rejected in the last transfer window.
RMC insists that pre-contracts have indeed been tabled, and it is now down to the player and his representatives to select the best offer.
Marseille have also offered Ayew a new contract, but they want the left-winger to take a significant pay-cut.
However, Ayew has his heart set on a move to England, with Liverpool his most likely destination.
Brendan Rodgers was interested in signing the 25-year-old last summer, but instead opted to splash the cash on the likes of Lazar Markovic and Adam Lallana.
But the former Swansea boss is now ready to bring Ayew to Anfield, with the view of deploying him on the left-hand side of Liverpool’s adventurous 3-4-3 formation.