AI said the groups had held "preliminary discussions" over a link which would create the country's largest producer of aggregates used in road building and heavy engineering.
Industry experts said any deal with AI, formed last year by the merger of Bardon and Camas, would force Tarmac to sell its construction and support services divisions, worth pounds 200m.
The announcement sent share prices in the two companies soaring, with Tarmac closing up 16 per cent at 93p, valuing the company at more than pounds 880m. AI finished 12 per cent higher at 63.5p, with a market value of more than pounds 760m
The sharp rises came despite an apparent attempt by Tarmac to dampen expectations. In a statement which did not mention AI the company, led by Sir Neville Simms, said it had been "in exploratory discussions with a number of the industry's key players".
Sources close to Tarmac said the company was looking at deals in a number of areas of its businesses. They said the company had not taken a decision on the construction and support services business.
A combined group would be the UK's market leader in the production of sand, gravel and crushed stone for construction and heavy engineering, with more than pounds 1.7bn in sales.
About 35 per cent of turnover would come from the US, where demand for aggregates has been boosted by a new law encouraging road building.
City analysts welcomed the prospective deal, but warned that the combined group's dominance of the UK market would almost certainly trigger a competition inquiry. They predicted that the merged entity would be forced to sell businesses in the North-west where it would have a near-monopoly.
"It is a sensible deal. Combining two large players would help to increase pricing power and push margins up," said Howard Seymour of ABN Amro. "If Tarmac don't do the deal because they want to keep the construction unit, shareholders would be baying for blood."
In the past two years, tough market and economic conditions have spurred a number of deals in Uk construction, including Tarmac's sale of its housebuilding activities to Wimpey in exchange for their quarrying unit and the acquisition of building materials producer Redland by Lafarge.
Investment, page 20Reuse content