It now seeks to build a shopping centre there instead as it moves away from the huge, eye-catching projects of the property boom years.
Ali Rashid Lootah, who became the chairman of Nakheel last March as part of its restructuring, said the developer was planning to build a mall on the strategic spot of Nakheel's best-performing project.
"We have to be realistic about these projects now," Mr Lootah said yesterday, referring to audacious plans such as the Palm Jebel Ali artificial island and the 1km-tall Nakheel Harbour and Tower. "There is no market demand for them. We will be selective."
The Trump project was first announced in 2005, but had its major unveiling at two expensive gala events in New York City and Los Angeles in 2008.
The Manhattan event was presided over by Donald Trump, the New York property billionaire who had lent his name to the project, and was attended by celebrities such as the supermodel Heidi Klum and actresses Demi Moore and Naomi Watts.
Mr Lootah said Nakheel had put on hold its most ambitious projects as the company completed its restructuring and focused on the "details" of running the largest property developer in Dubai.
The developer is also planning to cut service charges on its developments as it renegotiates contracts with suppliers.
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Under a restructuring proposal unveiled last year, the Dubai Government is injecting US$8 billion (Dh29.38bn) into Nakheel and converting a further $1.2bn of debt held by the Government into equity.
Nakheel is in the process of becoming a separate entity from the Dubai World conglomerate, which Mr Lootah said would happen by the end of next month.
The Dubai property sector was showing signs of a recovery, he said, with prices having dropped low enough for the emirate to be affordable for home buyers.
Since the beginning of the year, mortgage companies have been expanding their offerings, and prices in more established areas are stabilising, analysts say.
Prices in Dubai declined by 2.4 per cent for apartments and 5.1 per cent for villas in the final three months of last year compared with the same period in 2009, the property agency Cluttons said last month.
"Dubai is more affordable," Mr Lootah said. "Before it was expensive … Dubai still has something to offer. Fortunately enough we are ahead of everyone else in the region" in terms of infrastructure and lifestyle.
Offers and bidding prices for land on Palm Jumeirah have increased since last year, but Mr Lootah said the company had no plans to sell assets or property because of the oversupply.
"We will be the last one to do that," he said. "We are the biggest player in the market. If we start doing that, it will not necessarily be a good thing for the market. We have no plans for this in the near future … it would have a big negative impact. It will bring the prices down."
Some 7,800 units were completed in Dubai in the last three months of last year, bringing the total stock to 309,300 units, according to the property brokerage Jones Lang LaSalle. A further 25,000 units are expected to be completed this year, it said.
Nakheel is now focusing on improving operations, lowering costs through negotiations with service providers and completing a set of projects already started.
It is planning to begin an extension at the Dragon Mart shopping centre and the initial construction of the Palm Jumeirah shopping centre this year.
The developer has also restarted construction on the Jumeirah Park, Al Furjan, Jumeirah Village, Jumeirah Islands Mansions, Jumeirah Heights Clusters and Al Badrah projects, the company said last year.