The club's owners, the unpopular Glazer family, announced in November they were conducting a strategic review, with the sale of United one option on the table.
Qatar's Sheikh Jassim Bin Hamad Al Thani and British billionaire Jim Ratcliffe have made bids for the 20-time English champions.
Britain's Press Association said representatives of Sheikh Jassim were due in Manchester on Thursday, with Ratcliffe set to attend a presentation by senior management the following day.
Qatari banker Sheikh Jassim is aiming to take 100 per cent control of United and has attracted support from some fans by pledging to wipe out United's debt.
Boyhood United fan Ratcliffe's INEOS company is looking to gain majority control by buying out the stake held by the Glazers.
Neither bid is understood to have met the current owners' reported asking price of £6 billion ($7.2 billion).
Elliott Investment Management has also made it through to the next stage of the bidding process, although the US-based firm is said to be offering funding rather than a takeover.
The Glazers have saddled United with huge debts and have also overseen a major decline in the club's fortunes - last month's League Cup win at Wembley was their first trophy for six years.
Ratcliffe already owns French Ligue 1 side Nice and Swiss outfit FC Lausanne-Sport.
