The speculation follows a flurry of trading on Monday in which 13.7 million shares were bought and sold.
A City source said: "There's been a lot of trading in Amey this week, which leads to talk. Some people are talking about contractors eyeing up the firm – but I'm not so sure myself."
Laing O'Rourke has been tipped as a potential bidder, although this was strenuously denied by its management.
Last week, Building revealed that former Atkins boss Robin Southwell was preparing to head a bid for the support services company.
Southwell's former employer has also been the subject of intense speculation. City sources claimed this week that Atkins' QS arm Faithful & Gould was still considering a management buyout.
There has been a lot of trading in Amey, which leads to talk – but I’m not so sure
One source close to Atkins said: "There is a proposal on the table for the buyout. I would say it is about 50:50 as to whether it will happen."
The renewed speculation, which emerged after Atkins' shock profit warning last September, was played down by Atkins sources.
One said the group's future would be clearer once it had hired a chief executive and after a group strategy conference, which is due to be held in the summer.
The source said: "There has been talk about this for months. There has been proposal after proposal after proposal, from all sides of the business. Until a new boss comes in and a strategy is drawn up, the firm's future is up in the air."
The Atkins source observed that the group's performance and share price had stabilised in recent weeks. He said this could lessen the need for a quick sale.
The source added that the group was now moving away from the structure brought in by Southwell, who left the group last September.