Sheikh Jassim is in a bidding war with Ratcliffe after the pair emerged as the main contenders to buy the Premier League club from the Glazer family.
While Sheikh Jassim's latest offer is reported to be over £5 billion ($6.2 billion), the size of Ratcliffe's improved bid was yet to be made public when Friday's deadline for the third round of bidding passed at 2100 GMT.
Sources said Sheikh Jassim's bid for 100 percent control of the club comes with the promise of significant additional funding for transfers and infrastructure.
The spending would include either redeveloping United's out-dated Old Trafford stadium or build a new ground, along with overhauling the club's training facilities.
Sheikh Jassim's bid also promises to erase United's $620 million debt.
INEOS chemical company founder Ratcliffe, a boyhood United fan who failed in his attempt to buy Chelsea last year, reportedly wants to purchase a controlling stake in United of more than 50 per cent.
That would allow United's executive co-chairmen Joel and Avram Glazer to remain as shareholders with a 20 percent stake, which has raised concerns among a fanbase tired of the Americans' controversial reign.
The Glazers reportedly want a world record £6 billion fee for a sports club before they agree to sell the Old Trafford outfit, raising the possibility they might not accept either Sheikh Jassim's offer or Ratcliffe's approach.
Deeply unpopular with supporters since they saddled the club with debt in a £790 million leveraged takeover in 2005, the Glazers appeared ready to cash out at an enormous profit when they first invited external investment in November.
However, Elliot Investment Management and The Carlyle Group are among the private equity firms in the market for a minority stake that could allow the Glazers to retain control and provide the funding for investment in the club's infrastructure.
Avram and Joel Glazer are reportedly keen to hold on to their stakes in United, while siblings and fellow directors Kevin, Bryan and Edward Glazer and Darcie Glazer Kassewitz are open to offloading their shares.
Offers from the last round of bidding, a process run for the Glazers by New York merchant bank the Raine Group, were believed to have been worth a maximum of £5 billion.
That would have smashed the Premier League record of £2.5 billion paid for Chelsea last year by a consortium led by Los Angeles Dodgers co-owner Todd Boehly and private equity firm Clearlake Capital, with a further £1.75 billion promised in investment in infrastructure and players.
'Dire need'
The Manchester United Supporters' Trust (MUST) has called for a swift conclusion to the process to allow new owners to be in place for the summer transfer window.
"We are in dire need of new investment, which undoubtedly requires new ownership. MUST, along with United fans all around the world, are calling for this process to be concluded without further delay," the fans' group said in a statement.
United fans are believed to be planning a protest against the Glazers ahead of Sunday's match with Aston Villa at Old Trafford.
Decade of decline
Under the Glazers' ownership, United have been in a steady decline on and off the field over the past decade.
The Red Devils have not won the Premier League title since former manager Alex Ferguson retired in 2013, while the club's revenue has fallen behind local rivals Manchester City and Liverpool due to a lack of regular Champions League football and a failure to modernise Old Trafford.
But they are enjoying a renaissance under Erik ten Hag's management this season, having ended a six-year trophy drought by lifting the League Cup in February.
They also face Manchester City in the FA Cup final on June 3.
Just months after hosting the 2022 World Cup, a successful Qatari bid would give the Gulf state pride of place in the Premier League -- the world's most-watched domestic competition.
But Sheikh Jassim is the son of former Qatari prime minister Sheikh Hamad bin Jassim bin Jaber Al Thani, and his close links to the gulf state's ruling elite would raise questions over another Premier League club becoming a state-backed project.
Finnish tycoon Thomas Zilliacus is the outside contender, having recently said his offer from the second round of bidding still stood despite labelling the prolonged sale process as a "farce".
