Mr Wyllie has been in the role since 2005 when he joined from Taylor Woodrow - one of the companies believed to be in Costain’s sights.
He would not comment specifically on a bid for Taywood or rumours that he and Costain finance director Tony Bickerstaff - former finance director at Taywood - have been in to see Taylor Wimpey about a deal.
But he admitted to get into the top five the company would need to snap up rivals. He said: “We are constantly looking.”
Mr Wyllie said the firm has no debt and £133 million stockpile in the bank. He added: “I think the UK is contracting to a premier league of eight or nine tier one contractors - those who went for the M25 job.”
As well as Costain, bidders included Balfour Beatty, Carillion, Laing O’Rourke, Skanska, Vinci and Ferrovial.
Mr Wyllie said the benchmark for ambition was Balfour Beatty. Most observers expect it to be only a matter of time when parent Taylor Wimpey decides to sell the business, which in the six months to June saw revenue hit £346 million and make an operating profit of £900,000.
Costain’s turnover - less revenue it had from joint ventures - was just under £750 million in 2007, putting it in the top 20. According to this week’s Top 100, the company in fifth place is Kier with a revenue of just over £2 billion.
In the six months to June, Costain’s turnover was up four per cent to £467.5 million with pre-tax profits up a quarter to £10.1 million.
Analysis: Time for mid-table players to step up
By David Rogers
The idea of the super contractor has been in the mix for a long time now.
While Balfour Beatty has long since disappeared over the hill to become the industry’s equivalent of Chelsea FC - or should that be Manchester City? - followed by Carillion and Laing O’Rourke, a gaggle of contractors are faced with a choice. Acquire or be acquired.
Mr Wyllie is about right when he says there are no more than 10 major players in the industry.
The sort of clout Mr Wyllie has in mind echoes that of the foreign giants across the English Channel.
If anyone is best placed to pick up Taylor Woodrow it is Costain. It is inconceivable that it has not had a look at the business. Perhaps Taylor Wimpey hasn’t received a knock-out bid yet.
With Carillion calling a halt to its mega mergers, the onus will be falling on the second-tier of players to move up.