Ashtead rents out heavy machinery and equipment, such as cranes, excavators and scaffolding, to the construction industry.
With a stock market valuation of £24bn, it ranks among the top quartile of publicly listed companies in the UK, sitting directly behind NatWest in the FTSE 100 by market cap.
Though the board, led by chairman Paul Walker, is expected to take its time reaching a decision, City sources said there were a string of factors favouring a transatlantic shift.
More than 90pc of Ashtead’s near-£11bn annual turnover stemmed from sales in North America last year, up from 80pc in 2022.
This makes it the second-largest equipment rental outfit in the US, where it trades under the Sunbelt Rentals brand.
It also has operations in Canada and the UK, where growth has historically been much slower than in the US.
In March, Ashtead said it expected revenue growth of between 11pc to 13pc for the US and Canada, whereas that figure fell to between 6pc and 9pc in the UK.
Ashtead has also recently been a significant beneficiary of Joe Biden’s Inflation Reduction Act, which has made almost $370bn in tax breaks and subsidies available for green energy projects.
Chief executive Brendan Horgan has previously said the company was winning business tied to mega-projects such as “new electric vehicle manufacturing plants, the battery gigafactories to support that [and] liquid natural gas plants that are being built”.