A revival in London's office property market and Canary Wharf's expansion plans have stirred interest in Songbird.
Canary Wharf is preparing to start work on two major developments: a 60-storey tower with the first residential property on the estate and a 20-acre waterside site with 3,100 homes and office buildings, as well as a school and more shops.
However, Canary Wharf's complex ownership structure with two layers of shareholders, one in Songbird and another in Canary Wharf Group, has tended to leave Songbird shares trading at a discount to their net asset value.
Songbird owns 69.4 percent of Canary Wharf Group while U.S.-listed Brookfield, which operates and invests in office and industrial property, is the second largest shareholder in the unlisted company with 22.1 percent.
Meanwhile, Qatar's sovereign wealth fund owns 28.6 percent of Songbird. New York-based investor Simon Glick has almost 26 percent and China's sovereign wealth fund owns 15.8 percent.
QIA and Brookfield made a 2.2 billion pound approach for Songbird in November sending its shares soaring as much as 22 percent to 320 pence, but it was rejected.
Read MoreCanary Wharf-owner Songbird approached for takeover
In a hostile move, QIA and Brookfield took their new joint all-cash bid directly to shareholders on Thursday. Announced less than two hours before a deadline to submit a revised bid, it represented a 33.6 percent premium to Songbird's closing share price on Nov. 5, the day before the first approach.
Songbird said in a brief response its pro forma adjusted net asset value was 381p per share as of Nov. 27 and there were other areas of value within the company not reflected in that valuation. It said it would write to shareholders with its detailed view of the offer in due course.
Songbird's shares were down 3 percent at 313p by 0950 GMT, after an early rise to 335p fizzled out.
"Whilst we believe 350p is still too low and doesn't attribute any value to the future prospects or management, ultimately the shareholders have to decide whether they want to take the liquidity now or continue to invest in the longer-term outlook of what is arguably a unique estate at Canary Wharf," Miranda Cockburn, analyst at Oriel Securities, said in a note.
A successful bid would add to Qatar's significant presence in London. The Shard, western Europe's tallest skyscraper, and department store Harrods, are among its high-profile properties.
Clarification: This Reuters story has been updated since first published on CNBC to reflect that Songbird has announced it has rebuffed, not rejected, the offer.