West Ham, who have lost on their last six league visits to Old Trafford, thumped Liverpool 3-1 on Saturday the day before United twice lost two-goal leads and slumped to a 5-3 defeat at Leicester which left them 12th with one win from five matches.
That loss left United eight points behind leaders Chelsea, who face unlikely third-placed occupants Aston Villa at Stamford Bridge on Saturday, while Southampton, the early season surprise packages in second place, face struggling Queens Park Rangers.
The first Merseyside and north London derbies of the season also take place with Liverpool playing Everton at Anfield and Arsenal taking on Tottenham Hotspur at the Emirates.
Liverpool drew 2-2 with Championship (second tier)Middlesbrough in the Capital One (League Cup) before going through 14-13 after a marathon penalty shootout while Everton were knocked out 3-0 at Swansea City.
Arsenal were also eliminated when they lost 2-1 at home to Southampton while Spurs came from behind to beat Nottingham Forest 3-1.
Although league positions do not count for much at this stage of the season, form counts for a lot and West Ham showed their pedigree as goals from Winston Reid, Diafra Sakho and Morgan Amalfitano handed Liverpool a third defeat in five league games to leave them in 11th place.
England international Andy Carroll, their record signing, was asked if they could add United's scalp at a presentation about West Ham's move to the Olympic Stadium.
"One hundred percent we can. I don't see why not," said the injured striker who hopes to be playing again by December.
"You saw the way we played against Liverpool, the way we started, from the beginning, right from the off, and I don't see anything changing from when we go to United."
Even without Carroll, West Ham have scored five goals in their last two games which suggests another high-scoring match at Old Trafford.
United have netted seven goals in their last two league games but the five they conceded at Leicester has raised doubts about their ability to challenge for a top-four finish, let alone the title.
"I know United have spent 150 million pounds ($245.96 million) on new players this summer but I think they need to spend another 100 million in the next two transfer windows before they can even think about winning the title" former United defender Phil Neville said.
While United flounder, others are prospering and few with as much style as Southampton, who have won their last five matches and enjoyed an impressive 2-1 win at Arsenal in the League Cup, their first win there for 27 years.
"Of course, we have made a great start to the season, but it's how you finish the season that really counts. But we believe in ourselves and our results are proving that," coach Ronald Koeman said.
Spurs will try to emulate Southampton by winning at Arsenal, something they have done only once in the last 21 years.
They started the season well with four successive wins under ex-Saints boss Mauricio Pochettino, but drew two and lost two before seeing off Forest in the League Cup.
Leaders Chelsea warmed up for the Villa game with a 2-1 win over Bolton Wanderers in the League Cup and Manchester City crushed Sheffield Wednesday 7-0 ahead of their trip to Hull City.
Leicester travel to Crystal Palace, who won their first match of the season at Everton on Sunday and will be looking for their first home league win against Nigel Pearson's promoted side following a 3-2 loss to Newcastle at Selhurst Park in the League Cup.