The likelihood of one of these outcomes grew last week with the resignation of Brian Staples, Amey's chief executive, who had opposed a break-up.
However, analysts are warning buyers that the asking price may not be justified by the value of the company's contracts.
The concern is that the contracts may contain "change of ownership" clauses. These allow a client to terminate its agreement if the contractor is taken over by a third party.
Once the existence of these clauses are factored into calculations, contract values are unlikely to warrant Amey's pricetag, regardless of how it is offered to the market.
Amey's most important contact is with Jarvis and Bechtel, its partners in the Tube Lines consortium that will maintain and upgrade London Underground's Jubilee, Northern and Piccadilly lines. This agreement is known to contain a change of ownership clause.
Jarvis and Bechtel funded Amey's £60m stake in contract after Amey was unable to find the cash itself. Amey has until June to buy back its stake, but may not be allowed to do so if Jarvis and Bechtel are unhappy with a new owner.
It is not know how many other contracts have change of ownership clauses.
One City analyst said Amey's main resource was the expertise of its staff, and that if people were lost after a takeover, it might be enough to persuade clients – particularly local authorities under pressure to meet government targets – to cancel their contracts.
One major shareholder conceded that this was "certainly an issue".
Other analysts warned that, irrespective of the problem with change of ownership clauses, a break-up may not be the best way to maximise the value of the company.
One commented: "The problem centres on the value of the elements of the firm when you split Amey up. When you break it down you may find the individual parts are worth even less than you originally thought."
Staples resigned last week with a £287,000 pay-off. He was reluctant to leave, but a profit warning in December made his position untenable.