The runaway Bundesliga leaders have already confirmed the summer arrival of Pep Guardiola and are looking to add another feather to their cap with a £40m swoop for Suarez (pictured), according to Spanish newspaper Sport.
Meanwhile, Liverpool hope to agree the transfer of Philippe Coutinho in the next 24 hours despite the midfielder's claim that he wants to stay and fight for his place at Internazionale.
The Anfield club had a bid of around £8m rejected for the 20-year-old Brazilian last week but negotiations have continued and Liverpool are confident an improved offer will be acceptable.
Coutinho signed for Inter from Vasco da Gama as a 16-year-old, though he remained with the Brazilian club until he was 18, and is regarded as one of the most promising young players in Serie A.
Despite that reputation, Inter are considering the approach from Anfield as they look to improve their finances.
The player has placed responsibility for any transfer firmly on the Italian club by stating that he wishes to impress the coach, Andrea Stramaccioni. Coutinho said: "The Liverpool offer? I'm happy with these offers, because it means I am doing my job well. But I think Inter have faith in me and I want to show my value here. I don't feel that I'm on my way out. I hope to stay at Inter. The young players feel the faith of the coach and of the club."