The contracting giant confirmed preliminary talks had started in December.
And this morning it said: “The Group confirms that it is still in discussions regarding a potential acquisition of Mouchel.
“There can be no certainty that an acquisition of Mouchel will be completed. A further announcement will be made if and when appropriate.”
Any deal would follow on from Kier’s £221m acquisition of May Gurney in July 2013.
The latest announcement came as Kier revealed results for the six months to December 31 2014.
Group turnover ticked up to £1,583m from £1,432m last time while pre-tax profits dipped from £36.8m to £35.9m.
The construction division saw a significant jump in revenue from £742m to £874m with an underlying operating profit of £18m from £17.3m as operating margins dropped to 2.1% from 2.3%.
Chief executive Haydn Mursell said: “With improving economic conditions, and, notwithstanding pressures in the supply chain, our robust execution skills and delivery and disciplined approach to bidding and risk management continue to deliver good results.
“Now that May Gurney is fully integrated, we have a broad range of services across the Group and Kier is well positioned to work strategically with clients on how they can achieve their aims in light of financial challenges they face.”
Kier said a 7% increase in dividend payments to shareholders “reflects our confidence in the future”.