Sources close to the takeover said the 558p per share offer was still good but said that the lower price - after agreeing 585p per share in November- was due to stock market pressure.
Carillion said this was due entirely to a decline in its share price in the recent equity market downturn and that it had not found any problems in McAlpine's books.
The tie-up is also expected to provide around £30m in annual cost savings in the first year following the deal.
The deal will create one of the UK's largest support services and construction companies with an aggregate revenue of approximately £4.7bn. Carillion has said the two companies will offer an enhanced capability to provide “private finance, design, construction, maintenance and support services.”
Philip Rogerson, chairman of Carillion said: “We are confident this transaction can deliver significant value for the shareholders of the Enlarged Group.”