The job-seeking Bruno Senna visited Williams' Oxfordshire headquarters in recent days, Brazil's Globo Esporte reports.
The nephew of late Ayrton Senna, having started 2011 as Lotus/Renault's third driver, lost his race seat to Kimi Raikkonen and Romain Grosjean at the end of the season.
A return to the reserve role has been rumoured for 2012, and he has also admitted to contemplating a switch to Nascar.
But Globo reports that Senna, as well as team incumbent Rubens Barrichello, were both separately spotted at Williams' Grove factory this week.
The report said the 28-year-old underwent some physical tests and met with engineers at Williams, who still have a race seat vacancy alongside Pastor Maldonado for next season.
He apparently made a "good impression" on the famous British team, who are reportedly also interested in Senna's experience with Renault power, as Williams switches from Cosworth for 2012.
Globo also said Barrichello, who according to Auto Motor und Sport has amassed $5 million in personal sponsorship in a bid to keep his seat, was at the factory on Monday and Tuesday.
The report said the Brazilian veteran did not know about the candidacy of his countryman Senna.