The move is likely to result in Britain's biggest vehicle maker cutting agency staff at the plant near Birmingham as part of a manufacturing shake-up which is due to take effect from early next year as the European site at Nitra comes on line.
In 2016, the company said it would produce Discovery models in Slovakia.
JLR have said the decision to move production and the "potential" job losses was a "tough" decision to make.
Land Rover has discontinued the three-door Range Rover Evoque due to lacklustre sales.
Since then the company has revealed its profits were nearly cut in half in the fourth quarter as the car-maker was stung by a combination of falling diesel sales, Brexit uncertainty and vehicle taxation.
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The description also encouraged fans to watch the game's world premiere trailer, which has yet to actually premiere. The screenshots also give us a good look at Odyssey's map, locations, and tease a little bit of its naval gameplay.
Alongside the Slovakia announcement, Jaguar said it will invest millions in a revamp of Solihull, where the new Range Rover and Range Rover Sport models will be built.
A JLR statement also detailed plans for a refit at the Halewood production facility in Liverpool ahead of the next Range Rover Evoque's launch next year - meaning the entry-level Range Rover will continue to be produced at the plant.
The group saw pre-tax profit slump to £364million in the three months to March 31, down from £676million in the same period a year ago. It also has a factory in China and an assembly operation in India.
Diesel sales have been falling in the wake of additional surcharges and changes to VED introduced by the Government last April.
JLR has previously said its next-generation Discovery will be built at its Slovakia plant and on Monday announced there could be some job cuts in Britain as a result. It already employs 1,400 people there as it gears up to open.
The vehicle is now produced at a plant in Solihull, in the West Midlands.