Sheikh Jassim is aiming to take 100% control of the team, while Ratcliffe's INEOS company is seeking to gain a majority stake by buying out the Glazers.
Manchester United's potential sale is generating considerable interest, with two bidders due to hold talks with the club's current owners, the Glazer family, at Old Trafford next week.
The family announced in November that they were conducting a strategic review of the club, with the sale of United being one option on the table.
Qatar's Sheikh Jassim Bin Hamad Al Thani and British billionaire Jim Ratcliffe have both submitted bids for the club.
Sheikh Jassim is aiming to take 100% control of the team, while Ratcliffe's INEOS company is seeking to gain a majority stake by buying out the Glazers.
According to British media reports, representatives of Sheikh Jassim will meet with the United owners on Thursday, with Ratcliffe set to attend a presentation by senior management the following day.
The Glazers have overseen a major decline in the club's fortunes, and last month's League Cup win was their first trophy in six years. They have also accumulated significant debts for the club.
Neither Sheikh Jassim nor Ratcliffe's bids have met the Glazers' reported asking price of £6 billion ($7.2 billion).
Elliott Investment Management has also made it to the next stage of the bidding process, but it is offering funding rather than a takeover.
It remains to be seen whether the upcoming talks will bring the parties any closer to a deal.
Manchester United remains one of the most valuable football clubs in the world, and the sale could potentially fetch a record-breaking price.