If all goes perfectly, the 495-kilogram (1,100-pound) craft will slide gently on to the asteroid's rocky surface. It may bounce slightly before resting on its side, Dr Farquhar said.
Nasa has no idea whether the landing will work, but even if it does not the probe has more than fulfilled its mission objectives. The touchdown attempt is "bonus science", said Near mission director Dr Robert Farquhar.
"The unknown nature of the surface makes it hard to predict what will happen to the spacecraft, especially since it wasn't designed to land."
Near is currently orbiting Eros at an altitude of 35 kilometres (22 miles). On the landing day, it will fire its thrusters six times during a four-hour descent to slow down to one-to-three meters per second.
Gentle bounce
It is supposed to land gently at the edge of a saddle-shaped feature called Himeros.
If all goes perfectly, the 495-kilogram (1,100-pound) craft will slide gently on to the asteroid's rocky surface. It may bounce slightly before resting on its side, Dr Farquhar said.
It is also conceivable the craft will be smashed to pieces. Officials hope, however, that if Near does survive the impact, its antenna will still point towards Earth and its solar power panels will be functional enough to make some electricity. This would allow the robot craft to send back a beacon signal.
"If the burns (braking rocket firings) don't go properly, it would hit at about 30 km/h (20 mph)," said Dr Farquhar. "That would do us in."
God of love
Near was launched on 17 February, 1996, into an independent solar orbit. It swung by the Earth once to pick up speed and then streaked outward towards Eros, an asteroid in an elongated orbit that swings out to near Mars and back close to Earth's orbit.
In December 1998, a rocket firing designed to slow the craft and put it into an orbit around Eros failed and Near sped past the asteroid. But a second rocket firing series was successful and the spacecraft eventually slipped into an orbit around the asteroid, which is named for the Greek god of love, on 14 February, 2000.
Asteroid 433 Eros is 33 km (21 miles) long and 13 km (eight miles) in diameter.
It lies 315 million km (196 million miles) from Earth. Near-Shoemaker - Near stands for Near Earth Asteroid Rendezvous and Shoemaker honours the renowned US geologist Gene Shoemaker - has collected more than 160,000 images of Eros, about 10 times more data than originally planned.
Dangerous rocks
"We now know that Eros is a solid body of uniform composition, made of material probably older than the Earth," said Dr Andrew Chang, a Near project scientist. "Scientists will be looking at these data for years."
Dr Edward Weiler, head of space science for Nasa, said: "The mission is a total success story. It was started and completed in 26 months, from start to launch, for a total cost of $223m."
The spacecraft is helping astronomers to catalogue the potentially lethal space rocks that come close to Earth.
"We've really begun now the in-depth reconnaissance of so-called near-Earth objects," Dr Weiler said.
"These are objects that in the past have caused some bad days for some species on the Earth, namely the dinosaurs ... We do consider it a responsibility to learn as much as we can about these objects."