Earlier this month, Songbird, which owns 69% of Canary Wharf Group, advised its investors to reject the offer.
On Wednesday, it said it still believed the 350p per share offer was too low.
"The offer does not reflect the full value of the business, its unique operating platform and its prospects," it said.
Qatar Investment Authority (QIA) and US investor Brookfield Property Partners made the offer.
QIA already owns 29% of Songbird, but had to persuade the next three biggest shareholders, New York-based Simon Glick, sovereign wealth fund China Investment Corp and Morgan Stanley, who own more than 50% between them to accept the offer.
Songbird said it was now its understanding that "each of the major shareholders intends to accept the offer".
It also said the board had been in discussions with a number of parties "with a view to achieving a higher offer", but said it now believed none would be forthcoming before the 29 January offer acceptance deadline.
Canary Wharf was established 25 years ago as the new financial district in London, and is home to some of the world's biggest banks including HSBC and Barclays.
In the UK, Qatar owns Harrods, Chelsea Barracks and the Shard, Europe's tallest skyscraper.
QIA was founded in 2005 by the state of Qatar to help its economy by investing in a diverse array of businesses, outside of the country's huge oil and gas resources.
A Qatari-led bid has won the battle to take over London's Canary Wharf complex after three of its major shareholders agreed to accept the Â£2.6bn offer.