The Barclays 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 debts, the application said.
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 left debts of ?423million.
The club pursued a 1bn-dollar (?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.
Duncan Drasdo, chief executive of the Manchester United Supporters' Trust (MUST), welcomed the plan to reduce the club's debt.
But he questioned the value of the shares on offer compared with those owned by the Glazers.
Drasdo said: "A minority shareholding with inferior voting rights and no dividends is going to severely impact on the attraction to both financial and supporter investors.
"However, if it turns out that the vast majority of the proceeds are used to pay off the debt that is certainly something MUST would welcome and entirely vindicates our long-standing position that their debt was damaging our club."
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.