Kubica, who last competed in Formula One in 2010 with Renault, is attempting to make a miraculous comeback following a horrific rally accident back in 2011 in which he suffered a partially severed right arm.
The 32-year-old Pole, who has one F1 win to his name, tested twice for Williams last month in a 2014 car, the first coming at Silverstone while the second took place at the Hungaroring.
Senior figures at the Grove-based outfit are still unsure whether the Krakow-born ace can make a full comeback from the life-changing injuries so a third test is now expected.
It is understood Kubica will be tested at the official F1 Pirelli tyre test at Abu Dhabi in the week after the season-closing race at the Yas Marina circuit to get a clearer idea of his potential.
Williams are believed to prefer Kubica as the replacement for Felipe Massa, who is retiring at the end of the campaign, although Russian Daniil Kvyat, dropped by Red Bull last month, and Sauber driver Pascal Wehrlein are also in the frame.