The Sunday Times in London, without citing sources, said the US-based Glazer family was looking to kick off an issue in the city state after shelving its initial plans at the end of last year because of global market turmoil.
The report said with market conditions now improving, the club, currently top of the English Premier League, was looking at a listing of 25-30 percent of the shares, which would value it at up to 2.0 billion pounds ($3.2 billion).
The Glazers' financial advisers are believed to have suggested a listing before August, the report added.
However the source close to the deal, who asked not to be named, told AFP: "They are just waiting for the right time to press the button, but at the moment, the button has not been pressed.
"The IPO has always been on the drawing board. It was deferred last year because of weak market conditions but it has always been there," said the source.
"They just left it on the drawing board to be revisited at the right time."
The source said "there's a lot of speculation right now" on whether the owners of the club will proceed with the offer.
A Singapore listing would bring the club closer to fans in Southeast Asia, a football-crazy region of more than half a billion people.
Asia accounts for 190 million of the estimated 330 million United followers worldwide, and most of the club's sponsors are based in the region or generate a large part of their revenue from it.
United had earlier considered listing in Hong Kong and snaring the club was a coup for Singapore, which has long been in rivalry with the southern Chinese city as a regional financial centre.
But whether the club's fans will invest in droves remains to be seen.
"For the club, it's a good move to launch now. The market looks better now compared to last year when they wanted to launch," said Singaporean student Muhammad Nadjad Bin Abdul Rahim, 24, a United fan and part-time investor.
"Loyalty to the club is one thing, but I don't see any financial gains from buying the stocks," he told AFP.
"For blue chip stocks, you know what they are about and can make your decisions based on that... But in the sporting industry, you don't really know how they work, it's hard to make rational decisions like that."