The 300m-wide (984ft) rock, known as Apophis, will fly past Earth in April 2029 at a distance that is closer than many communications satellites.
Astrium, based in Stevenage, Herts, wants a probe to track the asteroid so its orbit can be better understood.
The concept will compete for a $50,000 (£25,000) Planetary Society prize, but a full mission would cost millions.
The British design calls for a small, remote-sensing spacecraft, dubbed Apex, which could rendezvous with Apophis in January 2014.
It would spend three years tracking the rock, sending data back to Earth about the object's size, spin, composition and temperature.
From this information, orbit modelling would enable a more accurate prediction of the risk of any future collision.
Astrium says that if its concept won the prize, it would donate the money to charity.
"The real prize for us would be if the European or US space agencies thought there was merit in our proposal and asked us to carry the feasibility study forward," said Dr Mike Healy, the company's space science director.
A full mission would be expected to cost several hundred million dollars to develop and launch.
Apophis caused some consternation in 2004 when initial observations suggested it might hit Earth in 2029.
Further study by ground-based telescopes indicated there was virtually no chance of this happening, and the expectation is that the object will whiz past the Earth at a close but comfortable distance of just under 36,000km (22,370 miles).
Talk of a possible strike on the next visit in 2036 has also been dampened by astronomers who have kept a careful watch over the rock's progress through space.
Nonetheless, Apophis is considered a good target on which to practise Earth-protection measures.
Were such an object to hit the Earth, it could cause devastation on a country scale, leading possibly to the deaths of many millions of people.
Scientists say, however, that given sufficient warning, a potential impactor could be deflected out of Earth's path.
Some have suggested such a rock might be nudged on to a safe trajectory by hitting it with a small mass. Others have proposed flying a spacecraft next to the object, to use gravity to tug the asteroid clear of the planet.
The issue of asteroid or comet strikes is a topical one as researchers continue to gather more information about their frequency during Earth history.
At least one of the planet's mass extinction events - which included the demise of the dinosaurs 65 million years ago - has been attributed to the impact of a large space object.
Liberal Democrat MP Lembit Opik has campaigned for the research area to be given more funding. His grandfather, renowned Estonian astronomer Ernst Opik, did much to raise science's understanding of Earth-crossing comets and asteroids.
The politician told the BBC News website: "The question isn't whether Earth is hit by an asteroid - it is when.
"Good luck to Astrium; they are showing that if we have the political will, we certainly have the technical know-how to do something about threatening objects."
The US-based Planetary Society has organised its competition in co-operation with the European Space Agency (Esa), the US space agency (Nasa), the Association of Space Explorers (ASE), the American Institute of Aeronautics and Astronautics (AIAA), and the Universities Space Research Association (USRA).
The winning entry will be submitted to space agencies to see if they want to carry the ideas through.