The Red Devils will return from the international break to face the Reds, who have yet to drop a single point in the Premier League. Their last outing before the next break, in November, will be against Brighton & Hove Albion.
Here is a look at the schedule, complete with predictions:
October 20: Manchester United vs. Liverpool, Premier League (1-2)
October 24: Partizan Belgrade vs. Manchester United, Europa League (1-1)
October 27: Norwich vs. Manchester United, Premier League (0-1)
October 30: Chelsea vs. Manchester United, Carabao Cup (2-1)
November 2: Bournemouth vs. Manchester United, Premier League (1-1)
November 7: Manchester United vs. Partizan Belgrade, Europa League (2-0)
November 10: Manchester United vs. Brighton, Premier League (0-0)
United entered the international break on a five-match winless streak across all competitions, putting a lot of pressure on Solskjaer.
The tactician said there was plenty of work to do after the 1-0 loss against Newcastle United:
Injuries were an issue before the break, and that trend could continue for the rest of October.
According to MailOnline Sport, star midfielder Paul Pogba is expected to miss the match against Liverpool:
His absence was felt in the draw against AZ Alkmaar and loss to Newcastle, with the lack of creativity in midfield a major issue. The Red Devils barely created chances in those two matches.
Liverpool are a daunting opponent even at full strength, but without Pogba pulling the strings in the centre of the park, things become that much harder.
David De Gea
The Red Devils will need vintage performances from David De Gea, who has yet to find his best form this season. The Spain international is among the world's best goalkeepers when on form, and he could be the key to a strong run before the next break.
United have conceded eight goals in the Premier League so far and haven't kept a clean sheet in their last three contests.
Apart from the clash with Liverpool, the schedule doesn't look too difficult in the next month. Chelsea are unlikely to field their strongest XI in the Carabao Cup, and Partizan Belgrade have shown weaknesses in their European campaign, including a loss to lowly Yeni Malatyaspor in qualifying.
However, De Gea's form should be crucial in the coming weeks, as his saves will be counted upon if the club's woes in attack continue.
Marcus Rashford, Anthony Martial, Daniel James
United haven't scored more than a single goal in a match since August, when they beat Chelsea 4-0 in their first Premier League match.
Anthony Martial and Marcus Rashford have so far failed to replace the production of Romelu Lukaku, who left for Inter Milan in the summer. Both finished with double-digit goals in the Premier League last season, so the talent is certainly there.
One player who has exceeded expectations so far is Daniel James, who has already bagged three Premier League goals. He hasn't found the net since the September international break, however, and he needs to get back on track in a hurry.
At least one of these talents needs to step up and find his shooting boots, or Solskjaer and his troops could be in for another poor stretch ahead of the next international break.