Roberto Firmino wasted the best of the home side’s opportunities in the first half when the Brazilian forward failed to hit the target with his three attempts.
Manchester United grew into the game in the second half but Alisson Becker was on hand to deny Bruno Fernandes and Paul Pogba in the final 20 minutes of the Premier League clash.
Pogba, in particular, failed to make his chance count with only the Liverpool FC goalkeeper to beat.
Ole Gunnar Solskjaer and Jurgen Klopp turned to their bunch in search of a winner but the two rivals ultimately settled for a point as Liverpool FC extended their unbeaten run at home to 74 games.