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.

Sailor Victor Magnus captured the scene when a ship carrying explosives caught fire in Halifax, Canada, resulting in the deaths of 2,000 people.
The explosion, on Thursday 6 December 1917, almost wiped out the town.
Mr Magnus's daughter, Anne Foreman from Cornwall, is to take the pictures to the Imperial War Museum in London.
It was 09:04 (GMT) when Halifax suffered the world's greatest man-made explosion at the time, when the two ships involved in the war effort collided.
Standing on the shoreline was Royal Navy Lt Victor Magnus.
The French ship SS Mont Blanc, which was loaded with wartime explosives, collided with the Norwegian vessel SS Imo.
The cataclysmic explosion occurred after a fire broke out on SS Mont Blanc, all of which was caught on camera by Mr Magnus.
SS Mont Blanc was described as a huge 'floating bomb' because of her formidable cargo.
There were more than 2,000 tonnes of picric acid, 200 tonnes of TNT, 56 tonnes of gun cotton and 223 tonnes of motor fuel on board.
Records show the ship exploded and disintegrated in seconds.
Altogether 3.8 sq km (1.5 sq miles) of Halifax was flattened and more than 1,900 people perished.
Avid photographer Mr Magnus managed to capture plumes of smoke and a town littered with ash in his photographs.
After the war Mr Magnus had three children. His daughter, Anne Foreman from Hayle, Cornwall, decided to share her father's photographs during the anniversary of the outbreak of World War One.
She said: "This has brought him to life again. It's amazing, it brings tears to my eyes.
Ms Foreman, aged 89, said her father was on watch during the morning of the explosion when he took the pictures.
"The blast absolutely blew Halifax town into oblivion, the whole of the harbour and the town was devastated.
"The thing that struck me most was a cannon that was blown three miles in land.
Ms Foreman said her father was "a kind and lovely man with a great sense of humour".
"There are so many things I've found out about him and his experiences from these photographs. I'm so happy he's been brought back to the forefront of our minds," she said.
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.
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Unseen pictures from World War One have been released showing what was then the world's largest explosion.