Speaking on stage at the Autosport International Show in Birmingham, Williams indicated that only small details needed to be resolved.
"It now is exactly that," she said when asked whether it was a question of 'crossing the Ts and dotting the Is' in the agreement.
Rosberg announced his retirement in early December, five days after winning his first title at the season-ending Abu Dhabi Grand Prix.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
His decision left champions Mercedes, the sport's dominant team, in a difficult position with all the other top drivers signed up to rival outfits.
Bottas was an obvious choice for his experience and existing contacts, with Mercedes team boss Toto Wolff previously a shareholder in Williams and also involved from early on in Bottas's management.
Former champions Williams also use Mercedes engines. However that team also needs an experienced driver to partner 18-year-old Canadian rookie Lance Stroll.
Brazilian Felipe Massa, a former Ferrari driver who has raced for Williams for the last three years and whose retirement was announced last season, is now expected to return as Bottas's replacement.
"I suppose as soon as Nico made his announcement, I knew the call was going to come from Toto," said Williams, who added that her team were amenable.
"For us, you don’t want to stand in the way of a driver who has the opportunity to go and race finally in a car that’s winning races, it’s winning world championships," she added.
Williams said Ferrari had also been interested in Bottas in 2015, when the team were determined to hold the Finn, who has yet to win a grand prix, to his contract.
"We need to make sure that if we are to release Valtteri, we have the best credible option to replace him with," said Williams.
"I wish I could announce who it was, we are still crossing the Ts and dotting the Is at the moment with all of the contracts.
"We will be making an announcement shortly because we are testing soon and we all want to know who’s going to be driving for us."
The season starts in Australia on March 26, with the first test of the new cars scheduled for Barcelona's Circuit de Catalunya at the end of February.
(Reporting by Alan Baldwin, editing by Ken Ferris)
