The possible offer is pitched at £20.80 per share, which would value WS Atkins at £2bn.
The UK firm says the bid is sufficiently high that it may recommend it to its shareholders, assuming a firm offer is made by 1 May.
Meanwhile the FTSE 100 index fell 40 points to 7,283, down 0.4%.
The biggest fall of the day came from Imagination Technologies, whose shares plunged 62% to 103p after tech giant Apple said it would end a deal to use its products.
The move by Apple, Imagination's largest customer, means the loss of lucrative royalty payments.
Imagination relies on Apple for about half of its revenues, with the US giant using the UK firm's chip technology in its iPhones, iPads, and iPods under a licensing agreement.
ITV fell 2.6% as the broadcaster's shares relinquished gains recorded last week after bid speculation.
Shares in ITV had jumped in late trading on Friday after suggestions that the company could be a takeover target for Liberty Global.
BP shares fell slightly despite announcing it had sold its Forties Pipeline System in the North Sea for $250m.
Earlier, the Markit/CIPS manufacturing purchasing managers' index fell to 54.2 in March, down from 54.5 in February.
A figure above 50 suggests the economy is growing, but the reading was weaker than expected.
The pound ended the day 0.6% lower against the dollar at $1.247, and 0.6% lower against the euro at 1.171 euros.
Shares in the engineering consultancy WS Atkins jumped 27% to £19.50 after a takeover offer from the Canadian engineering group SNC-Lavalin.