When asked about his plans for his rookie season, Kvyat told Russian television TV Rain: "I do not like to make such plans.
"I think you should always push to the maximum and see what comes of it.
"But I do believe that we have a good chance to fight for top positions, especially in a year when the regulations are changing so much.
"The middle teams will have the chance to get ahead, and I really hope they do," he added.
Some have linked Kvyat's promotion by Red Bull - over the arguably more experienced Antonio Felix da Costa - as an obvious nod to his Russian nationality, on the eve of the country's inaugural grand prix in 2014.
Kvyat admitted that he would welcome Russian backers to the Faenza-based team.
"It is a long process and not so easy," he explained, "but of course we are always open to negotiations with any sponsors.
"If there are interesting proposals we would consider them, as sponsors from Russia are very welcome."