Mesonero-Romanos said the Vison 2020 project is "what we target" after the launch of those cars.
He said: "It is not approved yet by the board, but if all goes well this car is a promise for the future."
Mesonero-Romanos describes the future design as "a big evolution from Leon", which is "even more sculpted with the lines, more brutal, tighter and more precise".
Seat has chosen to reveal this concept, which previews a model potentially so far away from launch, as a show of strength and confidence in the brand, and to show future ambition beyond it's already confirmed model plans.
"We don't just want to show the next car, but the next cars," Mesonero-Romanos said.
The concept car is larger than a Qashqai, almost 4.7m in length, making it the size of an Audi Q5. If it makes production by 2020 as expected, it will be a seven-seater. It is based on the largest version of the Volkswagen Group's versatile MQB platform, and could potentially be built on the same production line as planned VW and Skoda SUVs of the same size, despite its dramatic look.
Mesonero-Romanos said the starting point was ensuring perfect proportions for the car, particular in the side profile. The design mimicked the movement of a runner ready to surge forward by briefly rocking back on their heels, with a more 'cab back' profile and slight negative slope at the rear added to its dynamic stance.
The interior is also significant in showing how Seat will evolve the design from that of the current Leon. The interior style is instantly familiar from the Leon but altogether more futuristic, and controlled using what Mesonero-Romanos describes as a 'Seat Core'.
The Core is effectively a magnetic circular key that a user locks into the centre console, and the car's entire suite of interior functions - including driving modes, heater controls and infotainment options - are then loaded up, similar to a user profile of custom preferences on a laptop or smartphone.
Mesonero-Romanos revealed the tech was already up and running and had reached the point where it could be developed for production.
Seat boss Jürgen Stackmann said: "Design is already one of the most important reasons for buying a Seat and we intend to build on this strength, along with technology. Many details of the 20V20 will be evident in future production models."
These styling details include an X theme, which features on the front and rear of the car. A V shape on the bonnet means an upturned V in the grille, while at the rear the lines take in the tailgate and the rear bumper.
The show car’s length makes it 43cm longer than the Leon hatchback, while it features a 2.79m-long wheelbase and a 1.65m-wide front track. It sits on 20in alloy wheels and has a 22.8cm ground clearance. Seat has not specified precise interior dimensions, but says the 20V20 has more than 600 litres of luggage space on offer.
The boot also features a pair of luggage trolleys beneath the floor, along with something Seat is calling the Personal Mover. This is an electric scooter-like vehicle, which is designed to take the driver on the last stretch of their journey from the parking space to their destination.
Seat also says that the 20V20 is capable of accommodating a variety of different engines with petrol, diesel and plug-in hybrids all possible.
Seat also revealed at the show it was working with technology giant Samsung on future in car communications technology.