Earlier, we reported rumours from the Monaco paddock that the deal for the British team could be on the cards, because Renault was charging multiple millions more than Mercedes for a turbo V6 package.
"The decision is made and it will be announced this weekend in Monaco," said Swiss newspaper Blick's veteran correspondent Roger Benoit.
Germany's Michael Schmidt, of Auto Motor und Sport, is reporting similarly.
The Mercedes link is also an obvious one for Williams, with team co-owner Toto Wolff now the German marque's executive director.
And Wolff's wife Susie is the Williams test driver.
It is Williams' fifth different engine partner since 2005, hot on the heels of BMW, Cosworth, Toyota and Renault.