Both the governor of New York state, George Pataki, and the city's mayor, Michael Bloomberg, prefer Libeskind's jagged towers design to the other shortlisted proposal, a set of latticework towers designed by a rival practice, Think.
Libeksind's plans have also gained favour with the New York port authority, which owns the World Trade Centre site, and the Lower Manhattan development corporation (LMDC), which is overseeing the rebuilding.
Others on the corporation, including a close associate of President George Bush and the chairman of the board, are thought to favour Think's design, but it is unlikely that they will go against the wishes of both the mayor and governor.
In an increasingly fraught process, which has been dominated by inter-agency rivalry and public disaffection, Libeskind had to apologise on Thursday for voicing sharp criticism of his rival's plans in a live internet forum.
"There is a dramatic and urgent need to repair the skyline," he had said. "I do not believe that two skeletons in the sky asserts the vitality of New York or the courage of America. I do believe that a distinctive and economically viable skyline has to be built."
Libeskind's other works include the fêted Jewish museum in Berlin and the Imperial War Museum North in Salford, and he has been commissioned to make the spiral extension to the Victoria & Albert museum.
His design for the WTC is likely to be approved on Thursday, partly because it received considerable popular support for the amount of space devoted to the memorial, and for its striking use of light. "You look down, you see the void, you look up, you see light. In order to heal, you've got to have a scar," said one participant in a Municipal Art Society workshop last month, convened to encourage public participation in the process.
Another factor in its favour is that it will cost half as much to build. And Think's 85-floor towers have raised understandable security fears.
Officials are keen to point out that whichever design is selected will provide only a blueprint for whatever is finally built.
"These are plans that are to provide an inspiration for future development," the port authority's executive director, Joe Seymour, said earlier this week.
Some of the distinctive elements of Libeskind's design, such as a towering vertical garden, a series of jagged-edged office towers and the exposed pit to be left under the building as a memorial area, are unlikely to feature in the final stages.
"It's at this point when the plan collides with reality," the architect Craig Whitaker said. "The next phase in this journey is one that's going to be very difficult."
'Not cast in stone'
At this stage there have been demands for the pit to be made shallower, because the port authority would like to use some of it as a car park. The trade centre's leaseholder, Larry Silverstein, has openly questioned whether businesses want to rent space next to a hole that reminds them of their vulnerability.
Libeskind's proposal for a narrow 540-metre (1,776ft) tower, which would be the world's tallest building, topped by six enclosed botanic gardens representing different ecosystems, is unlikely to see the light of day.
"I think what people have got to understand is what comes out of this is suggestions," Mr Bloomberg said. "The buildings will be decided not on this plan necessarily, but by who wants to build them and where the money comes from and who wants to rent them, or live in them, or shop in them. It's not cast in stone."
Next week's announcement will mark the end of almost nine months of public debate about what should replace the World Trade Centre, balancing the interests of commerce with the need for a fitting memorial and the demands of residents in the Lower Manhattan area.
The first six proposals, unveiled in July, were so underwhelming that LMDC began all over again. It returned with a far more encouraging shortlist of nine models, including one by the British architect Norman Foster, which was ruled out last month as they whittled the competition down to two.
Central to the public and political discussions has been the issue of ownership. Responsibility for the site is divided between the governors of New York and New Jersey, who own the land, and Mr Silverstein who leased the space.
Although the LMDC is overseeing the process, it has no legal authority, and while the public's views have been taken into account, there is no structure to make their voices count.
The result has been a litany of both public and private rivalry between the various interest groups.