He said: "We need to maintain our growth and we want a good-quality services business that is property based, so we become a facilities manager who directly hires the cleaners and so on rather than contracting it out.
"That would give us more control over the standard of service. This could be M&E, waste, FM or landscape."
An acquisition would please the City, which has been waiting for Connaught to use its stock market listing to make a purchase. One analyst said: "Tincknell has been cautious, which is not necessarily a bad thing, but now it's time to crack on."
Connaught focuses on lucrative long-term contracts with local authorities, mainly refurbishing social housing and facilities management. It has a fit-out arm based in London.
Connaught's turnover has grown 151% since its flotation on the alternative investment market in 1998, and its turnover is set to top £100m this year.
Tincknell's goal is for it to reach £250m in three years.
The group's order book is up from £25m at flotation to £175m, of which £125m is long-term partnering agreements, mainly with local authorities for their social housing repair and maintenance.