Riyad Mahrez missed a penalty five minutes from time as the visitors continued their fifteen years winless streak at Anfield.
The game failed to live up to expectations with both teams seemingly comfortable with one point.
Both teams remain unbeaten in the league and now have 20 points -alongside Chelsea – separated by goal difference.
Liverpool started the better side and created the first chance of the game when Salah fired wide after receiving the ball from Gomez.
There were not much clear cut chances for the rest of the half as both teams walked in at half-time relaxed.
Much of the second half was same until the last fifteen minutes when City began to ask a few questions.
With fifteen minutes left, Alisson was forced into a double save after Bernardo and Sterling combined on the flank before the Portuguese flashed a cross the goalkeeper tipped away. Mahrez picked the rebound and played a low shot that was parried by Alisson.
Eleven minutes later, the Algerian was handed the chance to get City their first win at Anfield in 15 years.
Van Dijk brought down Gabriel Jesus in the box and the former Leicester man stepped up to take the penalty.
With three penalties missed from his last five, one would wonder why Mahrez selected to take the kick. He ballooned his shot over the crossbar as City failed to go two points clear.
Both teams will now turn their attentions to their next games in the Premier League after the international break.