Sir Jim Ratcliffe is reportedly prepared to offer the Glazers the chance to remain at Manchester United as part of his takeover bid.
The Glazers are currently entertaining offers for a full takeover and minority investment of the 20-time English champions.
Ratcliffe and Sheikh Jassim bin Hamad Al Thani emerged as the frontrunners in the first two rounds of bidding.
However, neither party met the Glazers' £6bn asking price, and as a result, the process has moved to a third and final round of offers.
The Raine Group are overseeing the transaction on the Glazers' behalf, and they have set a deadline for Friday at 10pm.
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Sheikh Jassim is keen to complete a full takeover of the club, while Ratcliffe has previously indicated that he wants to buy the 69% that is owned by the Glazer family.
However, according to The Times, Ratcliffe is proposing a new deal that could allow Avram Glazer and Joel Glazer to remain involved.
Ratcliffe would buy a controlling stake of over 50% for his petrochemicals company INEOS and allow the Glazers to sell entirely or keep 20%.
As part of the offer, the remaining 30% will stay with the various investment groups that already have a stake in the club.
The new proposal is likely to appeal to Avram and Joel Glazer, who are believed to be keen to retain an interest in Man United.
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A recent report claimed that Sheikh Jassim was still confident that his bid to buy the Red Devils would be successful.
There is also interest from several US investment funds that are looking to acquire a minority stake.
The Carlyle Group, Ares Management and Elliot Investment Management could all decide to submit proposals before Friday's deadline.
Meanwhile, Erik ten Hag's side are currently preparing for Thursday's Premier League away meeting against Tottenham Hotspur.
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