The main segment from the Long March-5b vehicle was used to launch the first module of China's new space station last month. Originally injected into an elliptical orbit approximately 160km by 375km above Earth's surface on 29 April, the Long March-5b core stage has been losing height ever since. At 18 tonnes it is one of the largest items in decades to have an undirected dive into the atmosphere.
Various space debris modelling experts are pointing to late Saturday or early Sunday (GMT) as the likely moment of re-entry. However, such projections are always highly uncertain. Most of the vehicle should burn up when it makes its final plunge through the atmosphere, although there is always the possibility that metals with high melting points, and other resistant materials, could survive to the surface.
The chances of anyone actually being hit by a piece of space junk are very small, not least because so much of the Earth's surface is covered by ocean, and because that part which is land includes huge areas that are uninhabited.
China has bridled at the suggestion that it has been negligent in allowing the uncontrolled return of so large an object. Commentary in the country's media has described Western reports about the potential hazards involved as "hype" and predicted the debris will likely fall somewhere in international waters.
But the respected cataloguer of space activity, Jonathan McDowell from the Harvard-Smithsonian Center for Astrophysics, US, said the situation did reflect poorly on China.
"It is indeed seen as negligence," he told BBC News. "This is the second launch of this rocket; the debris in Ivory Coast last year was from the previous launch, i.e. a basically identical rocket. These two incidents [the one now and the Ivory Coast one] are the two largest objects deliberately left to re-enter uncontrolled since Skylab in 1979."
Modern practice now calls for rocket stages to be de-orbited as soon as possible after their mission. In the case of large core segments, these would normally come straight back, within one orbit, falling into the ocean or on land (the US company SpaceX now propulsively lands its core stages so they can be used again).
For upper-stages that go into an orbit and may travel around the globe several times as they precisely position a payload, the preference is to include a re-ignitable engine that can steer the stage into a return at the earliest opportunity. Usually, this would be over an ocean - potentially in the furthest place from land in the South Pacific, between Australia, New Zealand and South America.