Andrea Leadsom and Andrew Lewer took the opportunity to lobby the multibillionaire after speculation about him visiting England to scout for a location for a possible new plant last month.
The South Northamptonshire and Northampton South MPs believe the county's numerous motorsport businesses and transport links make it the ideal place for Tesla.
Former business secretary Mrs Leadsom said: “Northamptonshire, at the centre of motorsport valley is a global force in high performance engineering.
"We have the talent, the infrastructure and the cutting-edge research architecture in high-end manufacturing and battery technology that makes Northamptonshire a very attractive proposition for global leaders like Tesla.”
The rumours were sparked when Mr Musk's jet landed at Luton Airport in May and the government asked regional authorities to prepare bids for a 250-hectare site for a major new car plant for an unknown company, according to The Daily Telegraph.
The two Conservative MPs are joining forces to keep a close eye on investment and business opportunities for the area, with one clear message of 'Northamptonshire is open for business'.
Mr Lewer said: “We highlighted in our letter the strengths of Northamptonshire strategic location at the heart of the UK strategic logistics and supply chain with Northamptonshire and the South East Midlands central to one of the most significant UK government regional investment programmes, the Oxford-Cambridge Arc, which will turbo charge our area’s R&D, science, technology and performance engineering capability on a global platform over the next decade.
"I am fully behind the Oxford Cambridge Arc programme with SEMLEP (South East Midlands Local Enterprise Partnership) and the new West Northamptonshire Council to make Northamptonshire and the region the best place in Britain for businesses like Tesla to locate.”
Mrs Leadsom added: “Motorsport Valley has around 4,300 companies that employs 41,000 people.
"It spends almost twice as much of its turnover on research and development than the pharmaceutical industry, in places like the Silverstone Technology Cluster in my constituency.
"Forward thinking and innovative automotive and mobility businesses would come here to benefit enormously by being so near such a powerhouse of research and high-end engineering capability.”