The game got off to a slow with both sides struggling to carve out clear-cut chances in the opening stages.
United were forced into two substitutions before the 25-minute mark as Ander Herrera and Juan Mata both picked up knocks and were replaced by Andreas Pereira and Jesse Lingard.
Five minutes later, the Reds were forced to make a change of their own when Roberto Firmino rolled his ankle and was replaced by Daniel Sturrridge.
The game's first chance arrived in the 40th minute when Romelu Lukaku picked out Lingard with a fine pass, but Reds goalkeeper Alisson popped up with a timely block.
The Reds saw more of the ball in the second half, but they were unable to penetrate to United defence as they did in the reverse fixture at Anfield a couple months ago.
With 70 minuets played, the Reds had a sight at goal as defender Joel Matip sent a header over the crossbar.
Xherdan Shaqiri and Divock Origi were thrown into the equation in the latter stages of the half as the Reds went in pursuit of late goal.
However, the encounter ended goalless as the point sees Liverpool leapfrog Manchester City into top spot, while the Manchester outfit drop out of the top four.