The supporters' consortium has put forward an offer to rival that of Andrew Ellis, a former director of the club and son of a former chairman, who is in talks with chairman Chris Wright, the newspaper said.
Ellis has been given two weeks to prove he has enough money to buy the club, which he wants to move to a new site near Heathrow airport, 16 miles west of London, from its current Loftus Road site in north-west London, its home for 70 years.
But the fans' consortium, whose bid is based on keeping the club at Loftus Road, says it has backing from a major investment company.
The paper reported the consortium as saying it could wipe out QPR's debts, which in May were said to amount to around £12 million ($17.03m/19.5m euros), and invest in the club's youth team.
A spokesman for the club's administrators told Reuters she could not discuss any bid until it was finalised.
She said, however, that any bidder for QPR would have to show proof of funds in order to be taken seriously.
The club has been struggling financially over the past year and was relegated at the end of the season.
Former chairman Chris Wright, the millionaire founder behind the Chrysalis record label, stepped down at the end of the season. He bought a controlling interest in the club in 1996 when QPR had just been relegated from the premier league.
He floated the holding company Loftus Road, an alliance between QPR and Wasps rugby club, but while the rugby team did well, winning the division one title in 1997 and the Tetley Cup in 1999, the soccer club continued to struggle.
Holding company Loftus Road cancelled its shares from trading on the Alternative Investment Market in April.
Fans of Queen's Park Rangers have launched a bid for the English second division soccer club, which has been in the hands of administrators since April, a London newspaper has reported.
