Kubica already has 76 Grands Prix to his name after spells with BMW Sauber and Renault between 2006 and 2010.
But the Pole switched to rally-driving and looked as though he might never drive again after an accident in 2011 which saw him suffer multiple compound fractures and a partial amputation of his forearm.
However, he made a return to rally action a year ago and was handed a chance to drive a Renault F1 car in July.
Renault boss Cyril Abiteboul was impressed by his form but they instead opted to replace Jolyon Palmer with Carlos Sainz.
And Kubica was subsequently given the chance to compete for the seat at Williams, with current incumbent Felipe Massa and reserve driver Paul Di Resta both also looking to the team for a job in 2018.
Kubica today completed his second day of running after a one-day test at Silverstone.
And while Williams were tight-lipped over the exact details of the day's action, they did confirm he had "completed another productive day" and the team would "continue our evaluation".
Current Sauber driver and part of the Mercedes junior scheme Pascal Wehrlein is also thought to be in the running to partner Lance Stroll but plenty of high-profile names have backed Kubica.
One of those is former F1 head honcho Bernie Ecclestone, who believes he could go right to the top of the sport.
"If Robert had not have had his accident, then I think by now he would have been world champion anyway," Ecclestone told Autosport.
"I think he can come back even stronger than before.
"Mentally, I think probably he will be more aggressive than he was then: so I can only see good, good things for him.
"In terms of his physical conditions, years and years ago, when I had a race team, we had a guy called Archie Scott-Brown who drove for us.
"Archie was bloody quick and he was in a worse position than Robert, much worse, and he managed to be very successful and b****y quick.
"I don't think his injury will hold him back."
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