BBC sports editor David Bond says it is understood the club has now lodged a listing application with the Singapore Stock Exchange.
Our correspondent says it could raise between £400m and £600m for the club.
It is understood the club wants to complete the listing by the end of the year.
The owners, the Glazer family, removed the Old Trafford club from the London stock market following their successful takeover in 2005.
A partial share sale, of between 25% and 30%, would also mean that no outside person could take control of the club.
At the same time, it would provide the Glazers with much needed cash that would help pay off some of the debt that was taken on to finance the takeover.
As well as the debt issue, analysts have seen a Singapore listing as an aggressive move by the club to create an even stronger presence in Asia.
United has more than 300 million fans around the world and more than 190 million of those are in Asia.
The region has become a growth area for the club and other Premier League teams.
David Bond said that the flotation would also be an opportunity to see what value the stock market puts on Manchester United, with an overall valuation of the club of anything up to £1.7bn.
The Manchester United Supporters Trust, which opposes the Glazer family’s ownership of the club, was suspicious about the flotation.
“The share sale will be in the Glazers’ interests – to pay down their debt – not the club’s,” said its chief executive Duncan Drasdo.
The Trust wants to see Manchester United owned by its fans, and is concerned that the Singapore listing could provide a “poisoned pill” to such hopes.
“By reducing the Glazers’ personal debt we will continue to be saddled with these absentee landlords,” Mr Drasdo added.
Despite the club’s hopes for a listing by the end of the year, according to the Singapore Stock Exchange (SGX) website, “depending on the complexity of the companies, the listing process may vary between four months to two years”.
And the SGX also says that any business seeking a listing will have to appoint a Singapore-based financial institution to be its sponsor and lead manager for the listing.
In March, Manchester United’s parent company said it made a loss of £108.9m in 2009-10. Red Football Joint Venture is the Glazer family parent company that owns the Old Trafford club.
Its loss for the year to the end of July 2010 included one-off costs from setting up a £526m bond scheme last January to replace outstanding debts of £509m.
There was also a drop in player sale income compared with the previous summer when Cristiano Ronaldo was sold.