The Russian has scored just four points compared to Sainz's 48 in a hard campaign, though the Spaniard's recently-announced 2018 switch to Renault appeared to have given Kvyat a better chance of staying put next season.
It had been reported that Sainz could join Renault as early as this term, but Jolyon Palmer's career-best sixth-place finish in Singapore appears to have saved the Englishman until the close-season, when he faces a battle for an F1 seat - Williams his most likely destination.
In recent weeks, Gasly's arrival at Toro Rosso was expected, but to replace Sainz, who has just signed at Renault for 2018.
Toro Rosso, who are switching from Renault to Honda engines next year, can ill-afford to lose Sainz with six races remaining.
"I will do my best to have good results with the Scuderia Toro Rosso during races to come".
Gasly, 21, who took the GP2 crown in 2016 before the championship was rebranded as Formula 2, has had to wait for his chance due to the wealth of talent in Red Bull's young driver program.
"He really has a valid chance of winning the title, as he is only half a point behind the leader".
Kvyat has not enjoyed a strong campaign in Formula 1 since being demoted from his seat at Red Bull to sister squad Toro Rosso, in order to make way for Max Verstappen midway through the 2016 season. "I feel as prepared as possible, having been prepared for everything in my role as the third Red Bull Racing driver this year". "For a variety of reasons, some related to technical issues, other to mistakes on his part, Daniil Kvyat has not really shown his potential this season, and this is why we put it aside for the next races", says Tost.
Red Bull could actually provide Gasly with two outings, in Malaysia and Japan, before recalling Kvyat for the US Grand Prix in Austin which clashes with the ultimate round of the Japanese Super Formula championship.
"The driver switch gives us an opportunity to make a more informed decision regarding our 2018 driver choices", the statement said quoting Toro Rosso team boss Franz Tost.