Jolyon Palmer is being linked with a potential move to Sauber for 2017.
The Swiss team's current drivers are Marcus Ericsson and Felipe Nasr, but both have been linked with a potential switch at the end of the year.
It is perhaps unlikely that Swede Ericsson will leave, because his backers are believed to be closely linked with Sauber's new owners.
However, Brazil's Globo quotes Ericsson as saying: "There is a vacancy at Force India and we'd be stupid to ignore it, because we don't have a contract for next year yet.
"Most likely is I will stay at Sauber, but as I said, I want to be in the best team and Force India looks very strong at the moment."
However, it is Ericsson's teammate Nasr who is most strongly linked with Force India, given the reported support of Bernie Ecclestone, who wants at least one Brazilian on the grid after Felipe Massa retires.
Nasr's move would leave a big sponsorship hole at Sauber, and so Switzerland's Blick newspaper says that at up to €4m (£3.6m) could be filled by Palmer.
The Briton is currently waiting on Renault's final driver decision, but sounding pessimistic.
"I'd love to be staying but the team are waiting to decide on the second seat," Palmer is quoted as saying by The Sun.
"Kevin [Magnussen] and I are trying our hardest in difficult car - it is not a good feeling. But I have improved a lot and know I have more to give in F1."
Palmer has picked up one point at this stage of the 2016 drivers' championship.
