George Russell, who is currently in his rookie Formula 1 season, is set to stay at the Grove outfit as he is tied to a multi-year deal.
Russell has previously asserted that he would only leave Williams for the 2020 season if he received a call-up from Mercedes, who manages his career - although any such promotion is now very unlikely.
Kubica has struggled against Russell throughout the 2019 season, following his comeback to F1 after his horrific rally crash in 2011, which left him with life-threatening injuries.
The Pole admits he doesn't know what he will be doing next year, although states that there are plans in the making.
“I don’t know what I will do in 2020,” he said at the Verva Street Racing event in Poland.
“There are no details yet. There are plans, but not everything depends on me. We’ll see how it goes. “The situation is like every year, it is necessary to be patient."
Williams reserve driver Nicholas Latifi, who is currently second in the FIA Formula 2 standings, is also believed to be in the running for a full-time seat at the team.
Williams is enduring a difficult season this year, as it is fighting at the back of the grid, far from the midfield pack.
Despite his difficulties in keeping up with Russell, team boss Claire Williams affirms that Kubica plays a vital role within the team, and fulfils the driver role that Williams needs to push its development.
"We needed a driver like Robert with his engineering and technical intelligence," she said.
"It's not an easy season for him, but neither Robert nor George is able to show all their skills in this car. But Robert is doing everything I expect from him."