Turner, 48, has been an assistant to coach Rick Adelman for 11 years with Portland, Sacramento and Houston.
Turner told Houston TV station KRIV on Wednesday that the Suns told him they would contact him next week if there were to be a second-round interview. Turner told the station he thought the interview went well.
Turner was known as a rugged defender in eight seasons as an NBA player. Improved defense is one of general manager Steve Kerr's goals.
Phoenix is seeking a replacement for D'Antoni, who resigned to coach the New York Knicks.