A source close to a major shareholder in Amey said the company had received a number of unofficial approaches from potential buyers, but Bechtel would be the favourite to buy it if investors decided to sell the group as a whole.
"Bechtel works on contracts with Amey, including the Tube, so it would make sense for them," the source said.
An Amey spokesperson said she was not aware that any approaches had been made. She said: "If there had been an approach that may or may not lead to an offer … then Amey would have to make an announcement to the market."
Another industry source said: "Bechtel would be an ideal buyer for Amey because it has acquired a reputation for turning round disastrous projects such as the Jubilee Line Extension, the National Physical Laboratory and the West Coast Mainline upgrade."
Bechtel is also a partner with Amey in the Tube Lines consortium bidding to take over one-third of London Underground.
A Bechtel spokesperson did not return calls from Building.
European construction giants Skanska, Bouygues and Vinci, which are all keen to increase their UK presence, are also believed to have made contact with Amey.
Bechtel would be an ideal buyer because it can turn around disastrous projects
Amey has become a tempting target because it is now valued at more than £70m, which is a gross underestimate of its worth.
The shareholder source warned bidders that investors would want a large premium on Amey's share price before they would be willing to sell.
"Amey has some very good businesses and contracts," he said. "That's where the value is, and that's why there are so many interested parties. The firm is really worth hundreds of millions so there will have be a major upside for shareholders to sell to one buyer."
Amey's road, rail and defence operations are the group's best businesses, and splitting them off from the less successful arms would generate money for shareholders.
Building understands that at least three venture capitalists are interested in buying parts of Amey.
Speculation that Amey would be sold intensified after the company announced last week that it had appointed City adviser Hawkpoint to "review the options for rebuilding the value of the group".
Another option would be for shareholders to hold on to their stakes in the hope that Amey's fortunes could be turned around. But the investor's source said lack of confidence in chief executive Brian Staples, who is refusing to resign, might lead shareholders to sell.