I will be disappointed if we haven't bought one or two by the end of the year."
The contractor has built up a fund for acquisitions after the sale of its housebuilding arm to Wimpey last year and aims to reposition itself as a support services company. It was linked with the sale of Thames Water subsidiary Subterra in May.
McAlpine announced a pre-tax profit of £14.8m for the first six months of this year, a rise of 23% on the same period last year. Group turnover has risen from £341m to £416.1m.
Chief executive Oliver Whitehead said: "We have had a successful first half and are on track to deliver a robust performance for the full year in line with expectations."
McAlpine does not intend to increase the amount of PFI work it undertakes because of bid costs. Grice said: "PFI projects are expensive to bid for and take a long time to close. We have just come second for a hospital scheme in Portsmouth that cost us £2m. We cannot afford to do that too often."
It has been named as preferred bidder for the £75m Addenbrooke's hospital PFI scheme in Cambridge.