Kubica, 32, has had multiple opportunities to test for Renault and Williams this year, and his latest will be at the wheel of the British team's 2017 car in the post-Abu Dhabi test.
Also in the running to replace the retiring Felipe Massa are Paul di Resta and Daniil Kvyat, and - contrary to the latest rumours - Pascal Wehrlein.
When asked about likely Sauber refugee Wehrlein, Williams boss Paddy Lowe told Auto Bild in Brazil: "Pascal is still in the race."
But Kubica would be the more popular choice, and Lowe admitted that it is a real possibility.
"We will almost certainly give him a chance to be in the car during one of the two days of testing in Abu Dhabi," he is quoted as having told German television Sky.
"The topic is getting a lot of attention from the media and fans, but it's something we're working on inside the team and don't want to say any more at this point," Lowe added.
Lowe also said Williams is determined to improve in the future, and one way to do that would be to take more parts from the team's engine supplier Mercedes.
"One idea is to get not only the power unit but also the transmission and drivetrain," Lowe admitted. "That would definitely help us to progress."