The Owls, who entertain Manchester City in the FA Cup third round this weekend, are still crippled by debts of £27m but are now mounting a push for promotion to the Premiership.
Allen describes the potential investor as a "multi, multi-millionaire" – which raises the possibility of a Roman Abramovich-style revolution at Hillsborough.
However, the club's second biggest shareholder, Wednesdayite, last night greeted the news with caution and said they would not be pressurised into selling their 10 per cent stake in the club.
Allen slapped a £25m price tag on the Owls earlier this season and turned down offers of investment from a consortium led by boxing promoter Dennis Hobson.
Three years ago he refused to sit down for takeover talks with former Chelsea chairman Ken Bates, who subsequently took control at Yorkshire rivals Leeds United.
A plan to raise £10m by building homes on the club's Middlewood Road training ground has been blocked by the local council so the emergence of the mystery Chinese businessman could yet be the answer to the club's financial problems.
Allen, who claims talks are due to take place in London later this month said: "This man has made money from casinos overseas and has vast wealth. At the moment, things are at a very sensitive stage, but someone like that on board would really help the club.
"We are not looking for small-time people, we are looking for a mega-rich businessman like Roman Abramovich at Chelsea who wants to buy a football club for a hobby," he added.
Allen claims that the Wednesday board, which currently owns 30 per cent of the shareholding, needs a 51 per cent stake to attract new ownership. Wednesdayite, however, firmly disagree and have turned down the offer to sell their shares for £500,000.
"In my experience investors want a return on their money," said Allen. "They would want control of the club for that kind of investment. There are one or two people interested in investing in the club but we have to have 51 per cent of the shares to be able to sell it on.
"I have been buying up shares and I will continue to do so. We need to reach that 51 per cent."
In a statement, Wednesdayite chairman Darryl Keys said: "Of course, we welcome and encourage any move by the SWFC Board to attract investment and do hope that the discussions are indeed serious and can progress.
"The club certainly needs a large capital injection, but we have to remain cautious until we hear more later this month as we've been in this territory before.
"If there is a serious suitor out there, then they will be used to approaching all major shareholders with their plans as is normal business practice in takeovers and acquisitions, so in that sense I do not see why Mr Allen needs to own our shares first to sell on to a new suitor a matter of weeks later."
Keys revealed that 90.13 per cent of Wednesdayite's members voted against the offer to sell the shares, which were originally gifted by the Owls board six years ago.
Allen has also been invited to address Wednesdayite members in a public meeting and explain why it is in the club's best interests that he acquires the shares personally but has failed to reply.
ian.appleyard@ypn.co.uk