The paper quoted an unnamed police source as saying the suspects had bought tickets for seats around the club's 67,000-capacity stadium for their premier league match against Liverpool on Saturday.
"The plot involved several individual bombers in separate parts of the stadium," the source told the paper. "If successful, any such attack would have caused absolute carnage."
Ten people were held under anti-terror laws in a series of dawn raids involving 400 police across northern England on Monday.
Police and the Home Office (Interior Ministry) declined to comment on the Sun's report.
"We cannot get into a running commentary on the intelligence and information behind police and security service operations," a Home Office spokeswoman said.
Assistant Chief Constable Dave Whatton, of Greater Manchester Police, said he was aware of "extensive speculation about possible targets".
"As with any counter-terrorist operation, we will not confirm or deny any targets," he said in a statement.
The Sun said the arrests were made after months of eavesdropping on mobile telephone calls and surveillance by British and American authorities.
Anyone planning an attack at Manchester United's Old Trafford stadium would have risked being frisked by security guards or police on their way into the ground.
An attack during the match -- one of the biggest games in the English soccer calendar -- would have been broadcast live around the world. The clubs are third and fourth in English soccer's top league.
Britain is on high alert for attacks after the Madrid train bombings which killed 191 people on March 11.
London police chief Sir John Stevens has repeatedly said an attack, most likely a suicide bombing, is inevitable.
Police arrested eight men and seized half a tonne of fertiliser often used in bomb-making in raids across southern England on March 30.
