Trading in the shares has increased dramatically over the past week after their price dropped more than 90% in the wake of last Tuesday's profit warning. This has led to a stabilisation in the price of the equity, albeit at a low level.
These developments have caused rumours in the City that a predator was buying shares in preparation for an asset-stripping operation.
It has also been suggested that Skanska and Bouygues, two of the largest contractors in Europe, are interested in Atkins, and that a management buyout at Faithful & Gould, its QS arm, is possible.
Jeffries angrily dismissed claims that the group, or parts of it, were up for sale and that investors were pushing for this.
"It is a temporary cash flow problem, that's all," he said. "Rumours are just rumours. If people thought about it logically … no matter what you are selling, you always sell from a position of strength."
It is a temporary cash flow problem. Rumours are just rumours
Atkins chairman Mike Jeffries
Jeffries said he did not know who had been buying the shares, although he added that some staff were taking advantage of the low price to increase their stakes.
City sources insist the pressure is on Jeffries, who is also the firm's acting chief executive, to do something to unlock shareholder value, such as some selling-off some of Atkins' profitable divisions.
One City source said Jeffries faced a dilemma. "The issue for Atkins is whether it tries to parcel something up quickly or tries to ride out the storm. I think the best route is to take it private."
Jeffries denied that going private was an option. He said: "It isn't on my agenda at the moment."
The City source added that a bid for the entire firm was unlikely. He said that the most attractive parts were its transport arm, QS Faithful & Gould, and estate agent, Lambert Smith Hampton.