Manchester United chiefs were impressed by the INEOS group during their meeting last week.
Sir Jim Ractliffe, the owner of INEOS, also had Sir Dave Brailsford alongside him during the session.
Per The Mirror, the group's familiarity with running elite teams, which include investments in Mercedes F1 and Nice in Ligue 1, could give them an advantage over the Qatari bid.
For their part, the Qataris also own Paris Saint-Germain, with UEFA said to have little problem with any ownership conflicts that may arise.
Both parties are expected to make improved offers in the coming week.
Ratcliffe stated in a Wall Street Journal interview that he would not be willing to overpay for United.