According to the Daily Mail, the pair, understood to be foreign students, look an official tour of the stadium on Friday, the day before the 1-1 draw with the Gunners.
They then hid in the toilets at Old Trafford rather than exiting with the rest of the tour group, and were only spotted the morning after.
United say there was no risk to safety, with all those who go on stadium tours searched beforehand with metal detectors, as well as their belongings, and counted in and out by tour guides.
United have launched an internal investigation with alarm bells triggered that two members of the public could remain undetected inside Old Trafford only hours before a 75,000 sell-out Premier League game.
The police were called but no arrests were made.
A United spokesman said: "We realise people will go to any lengths to watch a game at Old Trafford but these people went too far. The fact that they and their belongings had been searched before entry means we are confident there was no risk to safety."
It is the second breach of security the Red Devils have suffered this year after the final league game of last season was postponed after a bomb – later found to be a dummy device left behind after a training exercise – was discovered in a toilet.
Manchester United vs Arsenal player ratings
Manchester United vs Arsenal player ratings
1/22 David de Gea - 4 out of 10
With Arsenal scoring their only shot on target, it’s not been the best day for the Spaniard. He had very little to do throughout.
2/22 Antonio Valencia - 8 out of 10
Performed exceptionally today, looking strong going forward and defensively.
3/22 Phil Jones - 5 out of 10
Did the simple stuff well at the back, but looked slow defensively at times.
4/22 Marcos Rojo - 6 out of 10
Defended well throughout proceedings, played safely and used possession well from the back.
5/22 Matteo Darmian - 5 out of 10
A mediocre performance from the Italian. He was lunging into challenges, despite already being armed with a yellow card.
6/22 Michael Carrick - 5 out of 10
The skipper played a very standard performance today. He played his role well and stuck to his position.
7/22 Ander Herrera - 7 out of 10
His work rate was faultless and he influenced play in the middle of the park – good overall performance.
8/22 Paul Pogba - 6 out of 10
He appeared to patrol the middle of the park in the first half, but in the second half he seemed to go off the boil. He did not make many chances and lacked any attacking prowess.
9/22 Juan Mata - 8 out of 10
An exceptional performance from the Spaniard today. His goal was an example of his immense technical ability and he created chances throughout.
10/22 Anthony Martial - 6 out of 10
A somewhat quiet performance from him today, but he showed glimpses of brilliance in the first half with a number of strikes that tested Cech.
11/22 Marcus Rashford - 6 out of 10
Despite being caught out for the late Arsenal goal, his performance throughout was positive. He attacked confidently and his crossing was inviting problems for the Arsenal defence.
12/22 Petr Cech - 6 out of 10
He made a number of important saves in the first half, but was out of position when Mata broke the deadlock.
13/22 Carl Jenkinson - 4 out of 10
It was a somewhat uncomfortable performance from him today, as he looked slow and unable to keep up with the pace of the United strike force.
14/22 Laurent Koscielny - 6 out of 10
He did well in the air today, but the United attack got the better of him at times as he was caught out of position.
15/22 Shkodran Mustafi - 5 out of 10
It was an incredibly mediocre performance by the German. He did well in possession, but that wasn’t enough at times.
16/22 Nacho Monreal - 5 out of 10
A questionable penalty call in the first half was the main incident for the Spainard. He failed to show his defensive ability against the quality of United going forward.
17/22 Francis Coquelin - 6 out of 10
Made a number of important tackles, but it wasn’t enough to stop his opponents running the midfield battle.
18/22 Mohamed Elneny - 4 out of 10
The Egyptian made a few unneeded and mistimed challenges and failed to show any sign of threat when going forward.
19/22 Aaron Ramsey - 5 out of 10
He had very little of the ball throughout, and when he did he failed to do much with it.
20/22 Mesut Ozil - 5 out of 10
Taking into account his huge talent, it was a rather dim performance. He failed to create chances and feed Sanchez which resulted in Arsenal having no spark going forward.
21/22 Theo Walcott - 4 out of 10
A very quiet performance from the winger today. He saw very little of the ball and was regularly caught playing too narrow which left Arsenal with no width to their attacks.
22/22 Alexis Sanchez - 6 out of 10
He looked dangerous when in possession, but a lack of service did not allow him to make a real impact on the game.
The Daily Mail were told: “You honestly could not make it up. The two have gone on the tour on the Friday and for some reason, they must not have counted the numbers in and out and they have stayed there overnight without anyone seeing them.
“After the Bournemouth fiasco they retrained all the staff and beefed up security and searches but then this happens.”Reuse content