The 135 m high wheel, the largest of its kind in the world, hit trouble this week after the port authority said it had doubts over the feasibility of assembling it on temporary platforms in the Thames.
Once assembled, the plan is to hoist the wheel into a vertical position using a temporary crane.
The authority is concerned that the platforms, built 110 m out into the river, will affect the main navigation channel. It is midway through a four-week trial to test the project using temporary buoys to mark the extent of the obstruction.
"At this stage, we have reservations," port authority spokesman Colin Davis said.
"We are responsible for making sure the river is safe for navigation. If there are concerns and if it makes navigation difficult, then the harbour master has the ultimate sanction of saying that the project is not possible."
The South Bank site is opposite Westminster Pier and the authority is concerned that access would be too restricted during the wheel's construction. The pier is used as a base by 50 pleasure craft, and 3 million tourists pass through it each year. The proposed summer building period would exacerbate the problem because it would coincide with the height of the tourist season.
This area of the Thames is also used by barges and tugs – 800 000 tonnes of household rubbish are ferried past the site every year.
"Reducing the passage through the river by a half at that point is something we would have to look at very carefully. It is the busiest point in the river," Davis said.
Tim Renwick, director of wheel project manager Mace, said the project team would have to look again at its 31 December deadline if the port authority vetoed its plan to erect the wheel.
He said: "We've got a back-up plan, but it's obviously not our preferred method. We've had a long dialogue with the PLA about this, I would be very surprised if they said no."
The alternative is to build the wheel in vertical sections on the bank. Renwick said that this would probably have no impact on the project's £3m erection budget.
Mace said that assembling the wheel horizontally on platforms over the river would be safer than building it in a vertical position on the bank, as the latter would involve assemblers working at heights over long periods.
The wheel is the brainchild of husband and wife architects David Marks and Julia Barfield. Marks said: "We understand the reservations the authority has and we are addressing them."
He added: "It is a very busy part of the river between Westminster Bridge and Hungerford Bridge. But there have been other construction works into the river. The strengthening of the Bakerloo Line tunnels under the river involved works that extended across the whole of the river."
However, he said he believes the authority is sensible to express its reservations: "They are acting properly. It is a very complicated site and they have to be persuaded that we've taken all the various aspects into account. Our objective is to build the wheel in the safest way possible."
British Airways is the main backer of the £20m project. A BA spokeswoman said: "We are confident that we can reassure the PLA that this is the most satisfactory way to do it. We wouldn't be embarking on it of we didn't think it was safe."