The candidates for the purchase of the Red Devils had until 21:00 (local and GMT) to submit an improved offer compared to that formulated in mid-February.
The source contacted by AFP did not give details on the new proposal.
"Sheikh Jassim remains fully involved and confident in his offer. We think this is the best offer for the club, the fans and the local community," she said.
British billionaire Jim Ratcliffe, owner of petrochemical group Ineos and several football clubs, including OGC Nice in France, has also submitted a second offer, says the English press.
These two declared candidates had valued the English club around 4.5 billion pounds (5.1 billion euros) in the first round of auction, quite far from the 6 billion pounds (6.8 billion euros) expected by the American owners, the Glazer family, to cede control of the club.
The second offers reached or even exceeded 5 billion pounds (5.7 billion euros) according to several media, which is a world record for a collective sports club.
The continuation of the process launched in mid-November, when the Glazers said they were ready to explore "all options" on the evolution of the club's capital, is uncertain.
"The next steps will depend on the seller - we do not expect an immediate response," the source close to the matter said.
It is also possible that other non-public offers will be made to the American investment bank Raine, responsible for piloting the sale.
Sheikh Tamim bin Hamad al-Thani at an international conference on March 5, 2023 in Doha © KARIM JAAFAR / AFP
Several investment funds would be willing to make partial offers by allying with another investor or even to finance offers.
It is also not totally excluded that the Glazers, or at least Joel and Avram, who are co-presidents of the Red Devils, remain at the head of the club despite their very strong unpopularity, but raise funds to invest again, especially in infrastructure.
© 2023 AFP