The New York Times, the Financial Times and Reuters were among news agencies citing unnamed sources.
United was previously planning a $1bn (£635m) share sale at the Singapore Stock Exchange.
If the listing is moved, it would be the latest in a string of cancelled or delayed share sales in Asia.
The company could not be reached for comment, and the Singapore Stock Exchange declined to comment on individual companies when contacted by the BBC.
A report in Bloomberg news agency suggests the move is aimed at securing a higer valuation.
However, some analysts said the reason could be an attempt for Malcolm Glazer, the American owner of the club, to retain control by using a dual-class share structure.
US investors are more familiar with the dual-class share structure, which includes a separate series of non-voting shares.
United received approval for the Singapore share sale in September, but the process was delayed because of volatility in the stock markets.
Investor appetite has been dampened by concerns over the European fiscal crisis.
Last month, Graff Diamonds, a British retailer of gems, abandoned its $1bn share sale in Hong Kong.
Manchester United was bought by Mr Glazer in 2005.
Source: BBC News