Two other venture capitalists, Electra and Apax, are known to have examined a bid for the firm, possibly as long ago as last October. This was soon after the group issued a profit warning that sent its share price plummeting 72% to 52p.
On Monday Atkins confirmed in a statement to the London stock exchange that it had received an approach for the company.
3i is believed to be among several venture capitalists that have talked to Ric Piper, Atkins' former finance director, about a management buy-in for Atkins.
Piper has declined these opportunities. He said: "I have been approached by several very reputable venture capitalists. I am keen to get back into full-time executive work, but not for Atkins."
Cinven is thought to have considered the possibility of acquiring Atkins at the end of last year. Market sources said the venture capitalist's interest has since cooled as it would be a "very difficult" buy to calculate accurately.
The purchase is complicated by Atkins' blurred divisional structure and differing estimations of the value of its two major assets: employees and contracts. Market observers have put the value of the company at anywhere between £130m and £250m.
Two possible solutions to Atkins' problems can be discounted. Senior management does not want the company to be broken up, and a hostile takeover has been ruled out by the market as it would disturb the company's workforce.
A bid by a venture capitalist would recapitalise the firm and put it in a better position to grow; its net debt stands at £120m.
Market observers have estimated Atkins’ value at anywhere between £130m and £250m
Atkins chief executive and chairman Mike Jeffries said the talks with a potential buyer were "very, very preliminary".
Atkins' management is hoping to recruit a chief operating officer to eventually succeed Jeffries as chief executive.
A US market source said that one of Atkins' US arms, the multidisciplinary consultant Benham, was "getting close" to a management buyout.
The source said the Oklahoma-based firm, which was bought by Atkins in 2000 for £32.3m has recently been experiencing trading problems.
The source told Building: "Benhams has been in trouble, but Atkins has been a bad parent. There have been high demands on Benham but it hasn't received any investment."
Jeffries conceded that Benham had been suffering. He said: "The Benham business is having difficulties because its primary clients are Fortune 500 companies, and they generally are nervous about post-11 September, post-Enron, the Iraq war. The American private-sector is jittery."
WestLB and Gordon Morrison, a former owner of the construction arm, have set up a special purpose vehicle called Bream Investments to make a bid of 510p a share.
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