The Reds are eager to boost their attacking options and have already missed out on several high-profile targets, including Florian Wirtz and Nico Williams.
It's understood that Liverpool initially turned down a £58.6 million offer for Diaz, who has expressed his desire to leave the club.
Bayern's decision to make a second bid is reportedly linked to Newcastle's Alexander Isak, who has handed in a transfer request.
Isak is said to prefer a move to Liverpool, despite the fact that the club has already signed Hugo Ekiteke from Eintracht Frankfurt this summer.
Liverpool may need to break the British transfer record for a second time to secure Isak's signature, as Newcastle looks to cash in on its prized asset.