Ineos owner Sir Jim Ratcliffe and Qatari banker Sheikh Jassim will submit improved bids to buy Manchester United before Wednesday's 21:00 GMT deadline.
The two parties, the only publicly-declared bidders, met with United officials this month.
Both are understood to have held positive meetings while visiting Old Trafford and United's training ground.
Ineos want to buy the combined Glazer shareholding of around 69%, but the Qataris are targeting 100% of the club.
BBC Sport has learned that United officials met eight different potential investors over a 10-day period of high-level meetings recently, including Ratcliffe and representatives of Sheikh Jassim.
The amount of their initial bids have not been disclosed (with reports both are in the region of £4.5bn), but they are clearly far below the £5-6bn valuation that the club's American owners - the Glazers - have established.
Whether they - or any other prospective bidders - are able to submit an offer that persuades the Glazers to sell is the next key question.
If not, and with United's fortunes improving significantly in recent months under manager Erik ten Hag, the Americans may well yet decide to retain the club and perhaps instead look to sell a minority stake to the likes of US hedge fund Elliott Investment Management.
The Glazer family said in November they were considering selling United.
Announcing its initial bid Sheikh Jassim's Qatari consortium said the offer "plans to return the club to its former glories".
Described as a life-long Manchester United fan, Sheikh Jassim is chairman of Qatari bank QIB and the son of a former prime minister of Qatar.
The Ineos group, owned by 70-year-old British billionaire Ratcliffe, has a history of investment in sport and owns French Ligue 1 club Nice and Swiss club Lausanne.
Its sporting portfolio also includes high-profile sailing team Ineos Britannia - led by Sir Ben Ainslie - a five-year partnership with Formula 1 team Mercedes, and took over the British-based Team Sky in cycling in 2019.
At the time of the first bid it was understood its proposal would emphasise Manchester-born Ratcliffe would be "a British custodian for the club" and would aim to "put the Manchester back into Manchester United".