One of the most highly anticipated clashes of the football calendar began brightly, with both sides playing the game at a high tempo and getting early tackles in.
Chances were at a premium in the first half, however, with Paul Pogba firing from around 30 yards out on the quarter-hour mark and blazing over.
In the 54th minute, the Man Utd duo combined once again to greater effect, Pogba's cross from the right finding Ibrahimovic, but the Swede headed wide from eight yards out.
Two chances either side of the hour mark nearly saw Liverpool draw first blood, but De Gea was able to save from Emre Can's tricky shot, while substitute Adam Lallana fired wide moments after coming on.
With just a few minutes left, Antonio Valencia bailed his side out with a last-ditch tackle after Coutinho put Firmino through on goal with a defence-splitting pass.
Ultimately, the final whistle blew on a stalemate which saw the points shared between the two Premier League giants.
The result keeps Liverpool fourth in the Premier League, while Man Utd remain seventh in the table.