Ten agencies are believed to be involved. The account has been held for the last six years by Citigate Dewe Rogerson, with the account team currently headed by director Martin Jackson.
The successful agency will report to director of corporate comms David Paterson.
Investor relations director Neil Jamieson would not comment on the pitch process but said it was vital the firm's financial PR efforts communicate the company's expanded international focus to global financial communities.
Jamieson said: 'Clearly we have a far greater global presence and it's important that's recognised.'
Two years ago the British-based firm expanded its north American business with the acquisition of Agra.
It has also expanded in continental Europe, buying a stake in French contracting and construction firm Spie. AMEC is expected to exercise an option to buy the rest of the company in January next year.
Spie has this year been leading a consortium to build the controversial Yusefeli dam in Turkey. It is estimated that 18 towns and villages will be completely or partially submerged and up to 15,000 people displaced.
AMEC pulled out of the project last March citing commercial and human rights concerns, and environmental groups hope Spie will follow suit if AMEC takes control.