The Glazers expect new offers for Manchester United to be submitted on Tuesday.
The Sun says both Qatari banker Sheikh Jassim bin Hamad al-Thani and Britain's richest man, Sir Jim Ratcliffe, are in the running to buy the Old Trafford club from the Glazer family.
Other potential bidders have remained under the radar, although US hedge fund Elliott Management also visited the club after making its initial proposal.
Elliott, however, are seeking to provide finances for a bidder, rather than take control of United themselves.
Now, though, the next stage of the contest will begin in earnest with the would-be new owners asked to make their non-indicative" second bids.
These are more formal offers, expected to be higher than the initial valuations which were understood not to exceed 4.5bn.