David Stansfield, Hare's finance director and company secretary, said: "We couldn't agree on the terms of the takeover and it reached the point where we decided we couldn't take things any further. Basically, we couldn't agree on a final purchase price."
Stansfield said his company was not looking for other takeover opportunities but believed Amec would still be keen to dispose of Watson.
An Amec spokesman added: "We probably will still be looking to sell off Watson, as it is a non-core business."
Watson is one of the largest UK construction steel businesses, whose past projects include the Millennium Dome, Charles de Gaulle airport in Paris, Liverpool Street Station in London, the Scottish Exhibition and Conference Centre in Glasgow and football stands for Glasgow Rangers, Manchester United, Tottenham Hotspur and Bolton Wanderers.
It achieved less favourable publicity last year, when it pleaded guilty to health and safety breaches in connection with the death of a construction worker, who fell 130 feet inside a tower block at Canary Wharf.