A spokesman for Cable & Wireless said the firm was "actively considering" using the online reverse auctions for construction projects as part of a group e-procurement drive.
C&W chief executive Don Reed is expected to give the go-ahead to use the process for construction after the group saved more than £2m using the system in other sectors, such as purchasing computers.
A BP spokesman said that reverse auctions had been used across all BP departments. He would not be drawn on details of online construction tendering.
It is also understood that a leading housebuilder and a regional contractor are getting ready to start using the system in the north-west of England.
An e-procurement expert told Building the firms were in the early stages of looking at how the process works and were keen to start using it for M&E services.
The news comes despite complaints from specialist contractors, who say that the process represents a step back towards competitive tendering and runs counter to Egan principles.
Reverse auction bidding flies in the face of all the good Egan initiatives
Rod Pettigrew, legal adviser, HVCA
In reverse auction bidding the client invites prequalified firms to tender for work on the internet and just before the auction begins the client displays the lowest bid on a website. Firms have about 45 minutes to undercut this figure.
Rod Pettigrew, legal adviser to the Heating and Ventilating Contractors Association, is campaigning to stop the auctions spreading through the construction sector.
He said: "Reverse auction bidding flies in the face of all the good Egan initiatives." He added that it turned the clock back to lowest cost bidding, which failed to achieve value for money.
Pettigrew added that he was writing a report to present to HVCA members and hoped to meet companies using the process to highlight concerns.
The British Constructional Steelworkers Association has had reports from members about clients using the system.
BCSA legal director Marian Rich said she has been concerned about the procurement process since several members drew the issue to her attention.