Musk, who is chief executive of the electric car manufacturer as well as rocket company SpaceX, was reported by the Times to have arrived in to Luton on Friday and left late on Sunday. It was not noted how he avoided quarantine.
This comes a few months after business secretary Kwasi Kwarteng said the government is “considering and looking” at a site in south-west England.
It was reported that Musk last year took a look at potential sites in Somerset and the south-west of England for Tesla to continue its rapid expansion, after he took a similar trip in his Gulfstream jet to Bristol.
The Department for International Trade has approached local enterprise partnerships across the UK about information on large sites in the hope of enticing electric car manufacturers, The Times has reported, with sites of around four million square foot being wanted.
A new Whitehall department, the Office for Investment, has also been calling for regional authorities to submit locations for a potential factory for an unnamed company, according to The Daily Telegraph, with discussions having taken place over potential sites in the North-East and the West Midlands.
But Musk, when he was looking at a potential site in the Tees Valley last year, played down the possibility to building in Britain due to the uncertainty over Brexit.
Luton has a long history of automotive manufacturing, which has seen the Bedfordshire town used as a base for companies including General Motors, but its international airport means it is also associated with the airline industry, including housing the headquarters of easyJet.