A much-changed Liverpool side had the better of the chances over the course of the 90 minutes, but ultimately neither side could find a breakthrough as they set up a return fixture at Upton Park next month.
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The hosts made a quick start to the match, but West Ham soon settled and it was the visitors who were the first to come close when Dimitri Payet's cheeky free kick almost caught Simon Mignolet out at the near post.
The first chance of the match also fell to West Ham as Aaron Cresswell's delivery found Enner Valencia unmarked in the area, but the in-form striker got his header all wrong and could only nod it back out wide when he should have done better.
It was the aerial route that provided Liverpool's first openings of the match too, with Christian Benteke seeing one header cleared off the line at the back post before nudging another half-chance into the arms of Darren Randolph moments later.
Randolph was stretched into a more difficult stop with 10 minutes remaining of the first half, getting a fingertip to Cameron Brannagan's powerful 25-yard drive to send it just past the post.
The Hammers came close to breaking the deadlock in first-half stoppage time when the ball dropped to Pedro Obiang on the edge of the box and the Spaniard volleyed it narrowly wide of the target.
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It was the visitors who had the first opening of the second half too when Payet's free kick was flicked on by Nikica Jelavic, but Liverpool survived the goalmouth scramble that followed, as well as a penalty shout against Steven Caulker for handball.
Nathaniel Clyne and Joe Allen both had openings from outside the area that flew off target as Liverpool began to gain a measure of control in the match, and Randolph was called into action again shortly afterwards to deny a powerful Joao Teixeira strike.
The hosts continued to look the most likely to break the deadlock, but Benteke was not sharp enough to take advantage of a half-chance at the back post, before Randolph again kept out Teixeira.
A mixture of poor finishing and good goalkeeping was keeping West Ham in the match, and that was the case again 15 minutes from time when Randolph made a triple save to deny Benteke either side of an Allen effort, although Liverpool should have made more of the situation.
That proved to be the last clear opening of the contest as Liverpool added yet another fixture to their packed schedule, with the two sides now due to meet for the fourth time this season next month.