Sunday's visit of the Red Devils should see Liverpool break their Premier League home attendance record with around 57,000 supporters expected inside Anfield.
The new upper tier will be opened to fans if a test event on Monday evening runs smoothly.
An LFC Foundation mini-game and question-and-answer session with Jurgen Klopp will be attended by over 7,500 supporters at the Reds' home.
A further 2,000 hospitality seats and minor work to the Anfield Road Stand lower tier is expected to complete the refurbishment next month, at which point capacity will rise to 61,000.
That would break Liverpool's overall highest league attendance, which stands at 58,757 from a First Division draw with Chelsea in late 1949. The club's historic high attendance for a competitive home fixture stands at 61,905 from an FA Cup fourth-round win over Wolves in February 1952.
Work on the £80million upgrade was due to be completed for the start of the season but an initial delay was complicated by contractors Buckingham Group going into administration, leading to a phased reopening which has seen only the lower tier in operation.
"It's been really challenging," said Paul Cuttill, vice-president of Stadium Operations.
"Our priority was to get fans back into the stadium as soon as possible safely. Billy [Hogan, the chief executive] said back in October it would likely be 2024 before we would open so to get ahead of that for the Man United game is a bit of an early Christmas present.
"What it has cost us is the amount of time it has taken. Being able to bring in people earlier has been a massive benefit to us, but we won't know the true nature of the costs until we have got a proper programme in place towards the end of the season."