Both Ratcliffe and Sheikh Jassim have submitted multiple bids for United since the club's owners, the Glazer family, announced they were seeking "strategic alternatives" last November.
However, the British billionaire’s recently revised offer has given him the edge over his rival, Bloomberg reported.
The chairman of chemicals company Ineos Group is in talks with the Glazers and their advisers over the structure of a deal, Bloomberg said, citing sources with knowledge of the matter.
The report said Ratcliffe could make an offer for some of the shares held by both the Glazers and minority investors in Manchester United. Ratcliffe may end up with an initial stake of roughly 25 per cent in a deal that could value the club at more than £5 billion ($6.1 billion).
In June the club predicted record annual revenue for the 2022/23 season, raising doubts about whether the Glazers would sell.
United said it was expecting revenue to reach between £630 million and £640 million for its fiscal year 2023. Previous guidance was between £590 million to £610 million.
The record revenue could make the Glazers less keen to pursue a total exit from the club, suggesting Ratcliffe could gain the edge in negotiations over his Qatari rival.
Glazer ownership of Manchester United - in pictures
The Premier League club is widely seen as one of the most prized assets in all of sport. A $6 billion takeover would make it one of the biggest sports deals ever, following the similarly-sized sale of the National Football League's Washington Commanders earlier this year.
Deliberations are ongoing and there’s no certainty they will result in a transaction. While the Glazer family is believed to be close to finding a palatable deal, the situation remains fluid, and the Qatari group could still increase its bid, the Bloomberg report said.
Shares in Manchester United have risen 55 per cent in New York over the past 12 months, giving the club a market vale of about $3.3 billion.
Manchester United are the fourth-richest football club in the world, according to analysis by Deloitte.
The late Malcolm Glazer bought Manchester United in a 2005 leveraged buyout that saddled it with massive debts, and the family has faced distrust from supporters ever since.
While this was mitigated in the early years of their ownership as the team continued to win trophies under storied manager Alex Ferguson, resentment has grown steadily after the Scottish coach’s retirement in 2013.
United finished third in the Premier League in 2022/23, securing a lucrative return to the Uefa Champions League. United also won the League Cup and reached the final of the FA Cup before losing to crosstown rivals Manchester City.
They sit 10th in the Premier League table this season with 12 points from eight games.