Stockton has never coached on the professional level and retired from the NBA in 2003. He is the NBA's all-time leader in assists and steals.
Last month, the Jazz did not renew coach Tyrone Corbin's contract and he was let go after three plus seasons and a 112-146 record.
According to the report, other candidates include Chicago Bulls assistant coach Adrian Griffin, Jazz assistant Brad Jones, former Missouri coach and veteran NBA assistant Quin Snyder, and European coaching legend Ettore Messina. The coaching search could have as many as 20 candidates.
More from ESPN.com:
Jazz general manager Dennis Lindsey declined comment Tuesday night about Stockton or any other prospective candidates when reached by ESPN.com.
Earlier Tuesday, in a general interview with the Deseret News, Lindsey told the newspaper that the Jazz are "getting closer to moving to the part where we'll reach out" to coaches Utah will consider to replace Tyrone Corbin, who was informed last month that he would not be receiving a new deal. Corbin coached the Jazz for the past three-plus seasons in the wake of Jerry Sloan's sudden resignation in February 2011.