Sources say the Red Bull junior team will say this weekend at Sochi that the Russian driver is returning from his Ferrari test role to replace Pierre Gasly in 2019.
"If he does return then I think we will see a very different Dani," said his former teammate Daniel Ricciardo. "He was always fast and I am sure he has worked on his consistency."
Kvyat's 2019 deal is expected to be announced later on Friday.
As for the identity of his teammate, Brendon Hartley says he is in the running to stay in 2019 even though his season has been difficult.
"One or two good races and the headlines will be very different," he told Newstalk ZB. "I have a contract for next year and things can change very quickly."