United, currently top of the English Premier League, had planned to issue an initial public offering (IPO) in Singapore last year but deferred it because of poor market conditions sparked by the eurozone debt crisis.
The Straits Times, citing an unnamed source, said that with conditions now more favourable for a share float, the 19-time English champions are mulling which bourse to use.
The Singapore Exchange (SGX) approved Manchester United's application for a listing last year but they have not yet exercised the option.
The newspaper's source said the club had not yet decided to go ahead with its IPO, and was still considering Hong Kong as an option.
An industry source familiar with the deal told AFP that the report of a switch to Hong Kong was just speculation.
"If they decide to proceed and list in Singapore it will be a shorter route because they are already halfway there having been already granted by the SGX eligibility to list," said the AFP source, who asked not to be named.
If United decide to list in Hong Kong, they would have to go through the process of applying for permission with the southern Chinese city's exchange.
The Sunday Times in London earlier reported that United were looking at a listing of 25-30 percent of the club's shares, which would value it at up to 2.0 billion pounds ($3.2 billion).
The financial advisers of the US-based Glazer family which owns the club are believed to have suggested a listing before August, the Sunday Times said.