The team announced back in August that 17-year-old Max Verstappen would become the youngest ever driver in the sport when he makes his debut in the first race of next year's calendar.
Verstappen was due to partner Kvyat in 2015, but Sebastien Vettel's impending departure from Red Bull means the Russian will be promoted to drive alongside Daniel Ricciardo.
That leaves Toro Rosso with a seat to fill and although current incumbent Jean-Eric Vergne would appear the most likely candidate, team boss Franz Tost revealed they are looking at four potential drivers.
"There are also other drivers," he said. "We have Jean-Eric Vergne, which is an experienced driver, we have Carlos Sainz Jr which is currently leading the 3.5 litre Renault championship, then we have Pierre Gasly, we have [Alex] Lynn.
"Fortunately Red Bull has a lot of very fast, high skilled drivers in the driver pool and within the next weeks, Red Bull will decide who will get this seat."