Gasly has been well off the pace of the top five, consistently being outperformed by his teammate Max Verstappen, emphasising the gap between the two drivers. Gasly has over half as many points in the Drivers' Championship as Charles Leclerc, who is one place in front of him.
Kvyat meanwhile has shown more maturity than in his previous spells and has impressed at times at Toro Rosso. He has been linked with a return to Red Bull in place of Gasly but he played down the chances of it happening at this current moment.
“I do not look at other teams,” the Russian said at Silverstone on Thursday.
“When the right moment comes, we will look at next season, negotiate and make a decision.
"For now everything is very calm and develops as it should. I have no news on this topic.”
Gasly also told reporters that he is expecting improvements and changes across the board, saying: “What I listen to is what is said inside when we are together at the factory. I’m pretty confident we will see changes and improvements soon. There is not much else to say.”