Kubica trialled a 2014-specification Williams at Silverstone, which the Grove outfit labelled a "success".
Kubica has not raced in F1 since a 2011 rallying crash left him with severe injuries to his right arm.
'He showed in the Renault test he is ready and there's no doubt about that anymore.
But the French team decided against pursuing the Pole after signing Spaniard Carlos Sainz from Toro Rosso.
Ahead of next week's "shoot-out" with Paul di Resta in Hungary, Robert Kubica has completed a "successful" test at Silverstone today.
All a spokesman for the British team would say about the Polish driver's run in a 2014 auto was that it had been deemed a success.
The British team have one available seat alongside Canadian teenager Lance Stroll in 2018. Physically he is 100 percent in the vehicle, so it's a really exciting time, ' Rosberg told Sky Sports television at the weekend in Japan. I think it's more about getting to know each other and see if it's a good fit'.
"Williams want to take the fastest possible driver out there and this guy is seriously impressive with unbelievable speed so that is why he is being evaluated".
If the entirety of the test schedule rumor described by Motorsport is true, Kubica will again travel to the Hungaroring for a second test with Williams, for testing alongside Paul di Resta, though Williams has not publicly acknowledged this as part of their plan.
The spokesperson also confirmed that the vehicle used was the FW36, as the rumors alleged, but declined to comment on specifics of the test, including lap times, or the alleged comparison with current reserve driver Paul di Resta.
With both drivers having recent experience at the circuit, those tests are likely to give the team its best indication of the readiness of either driver. While Kubica and Di Resta are being evaluated, Massa is also hopeful of being retained for another season alongside Stroll.