Williams will finally reveal the identity of Lance Stroll's 2018 teammate on Friday.
With Felipe Massa retiring, the British team is the last on next year's grid to firm up their driver plans.
After a seven-year F1 absence due to injury, Robert Kubica was believed to have been the frontrunner, and Renault reserve Sergey Sirotkin then became a late contender, reportedly promising $15m (£11.3m) in sponsorship and going quicker than Kubica in the post-Abu Dhabi test.
Russia's Tass news agency now reports that Williams will end the long period of speculation by making an announcement on Friday.
"All Russian fans of motor sport hope very much to hear confirmation about Sirotkin and Williams in the very near future," Russian motor racing federation chief Igor Yermilin told Sportbox.
"As far as I understand, talks are proceeding and the management of Sergey and SMP Racing are working hard."
Kubica is now understood to be out of the running completely, with only Sirotkin's Russian compatriot Daniil Kvyat regarded as a remote 'Plan B'.
"Ideally we would like to see both Russians in the team, but unfortunately that is unrealistic," said Yermilin. "In any case, both are worthy of being race drivers for Williams or other teams."
Williams finished fifth in the most recent constructors' championship.