London-listed Amec employs 29,000 people in around 40 countries and generates annual revenues of £4.2 billion from markets including energy, mining and infrastructure.
Foster Wheeler has more than 13,000 staff in more than 30 countries, including in Aberdeen and its operational HQ at Reading.
Amec said it has provisionally agreed the terms of a cash and shares deal to buy Foster Wheeler for 3.2 billion US dollars (£1.9 billion). The combination would create a new company valued at £5 billion.
The two firms already work together after recently securing consultancy contracts in Kuwait for the building of a new refinery.
Amec said the tie-up with Foster Wheeler would more than double its revenues from growth regions, including through a boost in its Latin America exposure.
It will also extend its capabilities in oil and gas from exploration and production to the downstream sector, as well as bring in new customer relationships.
Chief executive Samir Brikho said the potential combination was "financially and strategically attractive".
He added: "I believe it would be a compelling proposition for our shareholders, customers and employees."
The making of a firm offer is subject to a number of pre-conditions, including completion of due diligence by both parties.
The move is the latest attempt by Amec to bolster its scale, having recently failed with a £700 million takeover approach for Kentz, which works on oil and gas services projects across the globe.
Foster Wheeler was formed in 1927 from a merger of two companies based in the United States - the Power Specialty Company and the Wheeler Condenser & Engineering Company, whose roots go back to 1891.