The new Audi TT quattro sport concept, an "extreme driving machine" capable of 0-62mph in 3.7sec according to its maker, has been unveiled at the Geneva motor show.

Dr Ulrich Hackenberg, Audi's chief technical officer, said, "With our quattro sport concept we wanted to demonstrate what the new TT’s technology can do if you take it a step further.

"We shall use it to achieve a new position for the TT, and also for racing," said Hackenberg. "The car will be a track-focused quattro GmbH product, but it will not be RS-badged. It's designed as an affordable Club Sport version of the TT rather than something like a GT3 car."

Audi's concept, which is based on the recently revealed TT, packs a 2.0-litre turbocharged engine that produces 414bhp and 332lb ft of torque.

That means the engine – which features a forged crankshaft, a newly developed turbocharger and a gas-flowed cylinder head – produces 207bhp per litre, eclipsing the likes of the Mercedes A45 AMG's 178bhp per litre.

"When I arrived at Audi I asked the engineers for more power from the 2-litre TFSI engine," said Hackenberg. "They offered 400bhp. I told them to keep going, so now we have 414bhp thanks to 1.8bar of boost."

Power is sent to all four wheels via a six-speed dual-clutch transmission and Audi's quattro system, with the resulting traction allowing the concept – which weighs 1419kg with a driver – to make best use of its power.

Audi has worked to improve the TT's dynamic capabilities too, with lower and stiffer suspension. Other upgrades include 20-inch alloys with centre-lock fitment, semi-slick tyres, a carbonfibre spoiler to boost downforce and a 'single-frame' Audi grille.

Inside, the interior resembles that of the series-production TT but features Alcantara trim, low-slung bucket seats, four-point harnesses and storage for two racing helmets.

The new Audi TT quattro sport concept isn't mooted as a replacement for the RS variant, but Audi has clearly suggested that it is now looking to do more with the RS's five-cylinder engine as a result of the quattro sport's output.

Hackenberg concluded, "The quattro sport is a car for the motorsports enthusiasts among our customers."

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Additional reporting by Andrew Frankel, 4 March 2014.