Sir Jim Ratcliffe and Sheikh Jassim will both submit second improved bids for Manchester United before an extended deadline, the PA news agency understands.
A cut-off of 9pm on Wednesday had initially been set for parties to submit revised offers and, after this was extended, both Ratcliffe and Sheikh Jassim both intend to meet the new deadline.
Ineos founder Ratcliffe and Sheikh Jassim bin Hamad Al Thani, the chairman of Qatar Islamic Bank and the son of a former Qatari prime minister, are the only bidders who have gone public with their intentions to complete a full takeover.
No figures have been revealed but one or more of the initial bids were reportedly in the region of £4.5billion.
That would make them world record offers for a sports club, but still some way short of the £6bn valuation reportedly placed on the club by current owners the Glazer family.
The Glazers acquired the club for £750million in a highly-leveraged deal in 2005. After a controversial reign, they announced they were seeking “strategic alternatives” that could include a sale last year.
Ratcliffe, who made an unsuccessful bid to buy Chelsea in 2022, visited Old Trafford last week.
The 70-year-old Ratcliffe was born in the Manchester area and is a boyhood United fan. He is one of the richest people in Britain with an estimated personal fortune of £6bn.
Sheikh Jassim has said his interest is a private initiative through his Nine Two Foundation and is not connected to the Qatari state.
His representatives also visited Old Trafford last week for talks, which were understood to be positive and constructive.
Little or nothing is known of other potential bidders but it reported that US hedge fund Elliott Management have made a proposal that would involve offering finance to either new bidders or the Glazers.