Tost told F1's official website that Kvyat has already revealed his championship potential within a few short races, which undoubtedly raises the pressure on Jean-Eric Vergne, Toro Rosso's established driver, who has been at Faenza since 2012.
But, for now, Tost is backing the low-profile 24-year-old Frenchman, insisting he is struggling with the new fly-by-wire braking.
"Jean-Eric is a quite sensible driver," he said, "and as soon as we have this (braking problem) under control I am convinced that he will show his real potential, because he is a really fast and highly skilled driver."
It is, however, an awkward time in Vergne's career, having been considered for Mark Webber's seat at Red Bull Racing but now seeing his former teammate Daniel Ricciardo perform so strongly alongside world champion Sebastian Vettel.
At the same time, Vergne is struggling to show up a boy-faced 20-year-old.
"A lot of things have been happening that were not necessarily visible," Vergne told France's L'Equipe, "but in these cases I prefer not to look for excuses but to keep my head down.
"I feel much better than last year in qualifying, even if the race results are not yet the ones we expected."
Still, he is keen to point out that when he was paired with Ricciardo, they were very closely matched.
"I have no regrets, because things happen for one reason or another," said Vergne, referring to Red Bull's decision to promote Ricciardo and not him.
"As I had the same performance as Daniel in the last two seasons, it shows what level we had, Daniel and me," he said.
"I learned a lot from him in qualifying, and in the race I was always able to make a difference."