He said: "The appointment of a chief executive will not be made before the end of the review. We are looking at the management structure and management of the group, so to get a new chief executive in before we know where we are going would not make sense."
Tutte's departure and the review of Wilcon's business followed a profit warning last month, caused by rising costs and poor sales.
After Tutte left, Leighton took over the day-to-day running of the company and promised to turn its fortunes around. Leighton also announced that former Alfred McAlpine Homes managing director Graeme McCallum, who is helping with the review, is to become a regional director. He will head the group's Northern, Midlands and Anglian businesses.
The City welcomed McCallum's appointment, saying more directors with housebuilding experience were needed on the main board.
An analyst said: "Leighton has obviously heeded the criticism that more expertise was required, and that's why McCallum has been appointed."