The company said Schroder Investment Management and New Star Asset Management will accept a possible offer for McAlpine shares.

The two investment companies own a total of 14.89% of McAlpine shares. The firms would accept an offer of 570p a share.

Schroder and New Star Asset will back Carillion if it makes a firm offer for McAlpine on or before 1 December.

Carillion said: “There is no certainty that any further approach to the Alfred McAlpine board, or any offer, will be made by Carillion, or as to the form of consideration of any such offer.”

McAlpine this morning said: "Whilst disappointed that Schroders has chosen to make this statement, Alfred McAlpine is aware that Schroders has a shareholding of 20.1% in Carillion."