Vick, who arrived at the Jets this off-season having lost his starting job at the Philadelphia Eagles last year, was widely expected to compete with Smith for the same role in New York.
Smith had a topsy-turvy rookie campaign in the NFL, but Vick believes that the 23-year-old is making a lot of progress and backed him to begin the 2014 season as starter.
"I would assume Geno would be the starter. Geno is making great strides," Vick is quoted as saying by ESPN.
"At the end of the year last year, he did a lot of remarkable things. He put his team in position to win and did everything he was asked to do."
Smith finished last year with 3,046 passing yards for 12 touchdowns and 21 interceptions.