A concept illustration of what Lilium's vehicles and ports might look like.

Lilium, a German electric flying car start-up, has hired a well-known designer to help bring its science-fiction concept to reality.

Frank Stephenson was behind the designs of cars including the new Mini Cooper, Ferrari F430, and McLaren P1.

He is now heading up design at Lilium, which is creating an on-demand air taxi service and his vision is to create a vehicle that people won't want to leave.

"If you get in a taxi, watch how quickly people get off, they don't waste time. You should walk away (from a Lilium jet) and the first thing you tell people is how much you enjoy the trip," Stephenson told CNBC in a phone interview Monday.

Lilium's idea is to create an app, like Uber, where a person can hail a flying car. Next year, it wants to have its first manned flight and then by 2025 have a fully-operational taxi service. The jet is able to vertically take-off and land, meaning it doesn't need long runways like an airplane.

Stephenson is focusing on the interior of the flying cars, the kind of stations that people will board from and, ultimately, how that will work.

The designer said there will be entertainment systems on board and materials that can turn opaque and then transparent. That would mean you could potentially change the floor of the jet transparent to see down to the ground.

He then described what the stations, where people can catch a Lilium jet, would be like.

"I envision them as ports," he said. "It depends on what you want to do. If you are in a city with a lot of infrastructure around, you won't have this land close to you where there are dogs and kids around.

"What you will probably do is go to a building with a rooftop that will have a facility for a very small area, much smaller than a helicopter, with a landing pad."

Lilium has a serious backer in the form of Chinese internet giant Tencent, which led a $90 million funding round in the German company last year.

But there is still a long way to go. Lilium's technology will require changes to aviation rules in many countries and will likely need to strike deals with governments to get its technology commercialized.

The start-up also faces competition from other air taxi firms. Kitty Hawk, the company backed by Alphabet CEO Larry Page, recently unveiled its flying car, with the CEO Sebastian Thrun telling CNBC in February that the vehicles could be in the air within five years.