WP declined to comment, with a spokesman saying the company never made any comment on media speculation.
Shares in WP soared more than 7 per cent or $1.37 to close at $19.89 after news of Egypt's approach to WP broke overseas.
If negotiations with WP are successful, the company would choose the technology and the site for the nuclear reactor.
WP would also be responsible for the quality control of the project, train staff to operate the power plant and provide other technical services, the Middle East News Agency in Egypt said.
WP was the under-bidder in a tender process to be a consultant on Egypt's plans to build its first nuclear power plant.
The tender was conducted by Egypt's Ministry of Electricity and Energy.
A ministry official told MENA an approach had been made to WP for a 10-year consultancy worth (US)$180 million. MENA did not explain why negotiations between the ministry and the tender winner, Bechtel Power failed.
Egypt plans to build several civilian nuclear power stations to meet its escalating energy needs.
WP has extensive experience in nuclear power plants in Bulgaria and North America.
In Bulgaria, WP is the owner's engineer for the nuclear power plant.
The 10-year project started in 2005 and, when completed in 2015, the Belene nuclear power plant will help Bulgaria comply with the Kyoto Protocol and strict European Commission release regulations.
Australia has one nuclear reactor, a small scientific facility at Lucas Heights, 31km southwest of Sydney, which is used for medical applications and experiments but generates no power.
WP had a small consultancy role in Lucas Heights' new reactor completed in 2007, a spokeswoman for the Australian Nuclear Science Technology Organisation confirmed.