Balfour Beatty makes agreement to buy two of Mowlem's businesses if Carillion bid succeeds.
However, in a statement to the stock exchange it said that it had "reached a binding agreement" with Carillion that if the latter's recommended £313m, or 220p a share, bid for Mowlem succeeded, Balfour would buy two of Mowlem's businesses - Edgar Allen and Charter.
Edgar Allen is a UK rail track products manufacturer and Charter is a US-based construction management company. Balfour has agreed to pay a total of about £20m to Carillion for the two businesses.
The Takeover Panel had given Balfour Beatty a deadline of today to declare whether or not it would be making a rival for Mowlem, after it initially said it was a possibility on 12 December.
In 2004 Edgar Allen made a £2m profit on a £25m turnover. Charter, which is based in Texas, made a £2m profit on £95m turnover in the same year.