Rugby, which said it received an approach from an unnamed company eight days ago, was linked with RMC in a spate of weekend press reports.
Neither company was yesterday prepared to comment on a potential deal, which follows last week's pounds 1.3bn agreed takeover of aggregates group Tarmac by Anglo American, the South African mining group.
If successful, a Rugby-RMC transaction would mark the first time in Britain that an aggregates and concrete producer has combined with a cement manufacturer. Cement is one of main ingredients in concrete, along with sand and gravel.
The tie-up could have knock-on effects for the industry's other key players, including Blue Circle Industries, Britain's largest maker of cement, which has struggled in recent months as its overseas operations have underperformed.
Rugby's shares closed at 118p on Friday - 3.5 per cent up since the bid talks were announced - capitalising the company at pounds 769m. It is understood that Peter Johnson, Rugby's chief executive, would be prepared to seal a deal at about 130p a share, or pounds 846m.
In recent weeks, Mr Johnson has been hinting that he would be prepared to accept an offer for the group after overseeing a string of deals to re-focus the company on core building material operations. Last month, Mr Johnson said: "Over the last nine months, we will have concluded the deals that we set out to ... [but] this is an industry where financial scale and industrial scale matters. We are undersized on both counts."
Analysts say that the pressure for him to conclude a merger or agreed takeover has been building as the refocusing has drawn to a close. "It's now basically a pure cement play, and they either need to get bigger or get out," one said.
In October, Rugby merged its US building-material and millwork business with Huttig, a subsidiary of Crane Co, a US group. It has also sold off its UK, Australian and European joinery interests for a total pounds 138.5m.
RMC has had a tough year, with performance hit by a severe downturn in its German business. RMC shares closed at 910p on Friday after surging 55p.Reuse content