The Premier League club filed documents with the United States government's Securities and Exchange Commission on Tuesday.
Share prices have yet to be set, but United would use the money raised from the flotation to reduce its enormous debts, the application said.
United have said they do not intend to pay dividends to investors, who will also have diluted voting rights.
The flotation would leave control over the club in the hands of the Glazer family, the billionaire US sports investors who bought the club in 2005 for 1.47bn dollars (£940m) - a takeover which saddled the club with debts of £423 million.
The club pursued a $1 billion (£640m) flotation on the Singapore stock market last year but the move was halted because of the volatile global economy.
Under the reorganisation, the team would become a wholly owned subsidiary of Manchester United Ltd, a newly formed holding company based in the Cayman Islands.
In April, Manchester United was valued by Forbes magazine at 2.24bn dollars (£1.43bn), making it the most valuable club in world football for the eighth year in a row.
So far, the Glazers' takeover of United, which they achieved by borrowing £525m, has cost the club more than £500m in interest, bank charges and fees.