Bayern are after a bit more fire-power going forward as they look to win both the Champions League and Bundesliga this campaign, so Suarez might be a great bit of business for them.
However, if a deal did go through, it is thought the German giants might have to wait until the summer to secure the services of the Uruguayan.
Pep Guardiola is of course taking charge at the Allianz Arena in the summer and he looks like making the Liverpool striker his main target in the transfer window.
Suarez has 20 goals in 30 appearances for the Reds this campaign and is second to only Robin van Persie in the English Premier League golden boot standings.
Liverpool are sure to do all they can to keep their number seven at the club, but if Bayern do offer the £40 million that is being reported, it might be tough to turn it down.
If the player wants to go as well, then this deal could be all but tied up by the end of the campaign.
We shall see.