The Tesla CEO's private jet landed at London Luton Airport earlier this week, as his firm continues global expansion plans, the media reported.
One of the possible sites is rumoured to be the 650-acre Gravity industrial park in Bridgwater, Somerset.
The Department for International Trade (DIT) is on the hunt for a location for vehicle research, development and manufacturing "gigafactory, it is understood, reports the mirror.co.uk.
According to a UK magazine Property Week, officials are looking to secure around four million square feet of industrial space for a mammoth plant.
The trade publication also revealed that clean energy and car company Tesla is linked to the search.
After Shanghai in China, Musk has chosen Berlin as Tesla's next gigafactory outside the US where the company is planning to invest 4 billion euros ($4.4 billion) and produce 150,000 cars a year.
Musk-owned electric vehicle (EV) maker is also planning to build its next Gigafactory to produce Cybertrucks in or near Austin.