Bayern arrived on Merseyside having remained undefeated through the group stages while they had won six and drawn two of their previous eight away days in Europe, although Liverpool boasted an unbeaten run of 19 European games on home soil ahead of this fixture.
Therefore, it was no surprise that there was no separating the two sides on the night with Liverpool enjoying the better of the opportunities only to uncharacteristically lack the clinical finish in the final third.
But, the fact Liverpool kept a clean sheet will be a boost as they travel to the Allianz Arena for the second leg knowing an away goal could be vital to their hopes of reaching the quarter-finals.
Reds boss Jurgen Klopp made two changes from the side that beat Bournemouth 3-0 last time out as Trent Alexander-Arnold and Jordan Henderson came into the side in place of James Milner and the suspended Virgil van Dijk.
Bayern boasted just one change from their 3-2 win against Augsburg on Friday, as Leon Goretzka was replaced by Javi Martinez.
It took until the 12th minute for a chance of any note as Henderson lifted a superb ball over the top for Mohamed Salah to run on to, but his first touch was poor and it rolled through to Manuel Neuer.
Bayern responded immediately with Serge Gnabry’s cross into the area inadvertently headed towards his own goal by Joel Matip, but Alisson fortuitously managed to make the save as the ball deflected wide off the Brazilian’s face.
On 16 minutes Naby Keita picked out Sadio Mane in the area but he dragged his effort wide, before an error by Alisson at the other end almost gifted an opener to Kingsley Coman who could only hit the side-netting with his subsequent strike.
Liverpool went close on 24 minutes when Bayern failed to fully clear their lines and Alexander-Arnold’s lifted ball to the back post dropped to Salah, but the usually prolific forward put his header just wide.
Mane should have put the hosts in front 10 minutes later when he fired wide from close range after Niklas Sule’s block from a Keita effort dropped invitingly at his feet.
Alisson was forced to make saves from both Gnabry and Robert Lewandowski, before Matip fired a shot just wide from six yards following a Roberto Firmino pull-back at the opposite end on 42 minutes.
Liverpool looked the more likely in the opening stages of the second half, but again were guilty of missing a gilt-edged chance on 55 minutes when Andrew Robertson’s cross-shot rolled towards the back post and Salah dinked his effort wide with Neuer doing his best to put him off.
Gnabry had Bayern’s next chance on the hour as he let fly from 20 yards out which just cleared Alisson’s crossbar with the Reds shot-stopper scrambling across his area.
Liverpool continued to do the majority of the running as they looked to secure a first-leg lead but Bayern defended resolutely throughout.
The Reds had a couple of half-chances late on with Matip lifting a shot over the top from the edge of the area, before Mane spurned another opportunity on 85 minutes with a low header from a Robertson cross which Neuer got down well to save.