But the franchise's all-time leader in assists in passing on a full-time coaching role.
ESPN and USA Today reported Nash is not considering becoming a head coach.
Nash, who serves as a part-time assistant for the Golden State Warriors, could also be in the running to be hired by Sarver in more of a front-office role.
The Suns fired Hornacek, another former guard from the franchise's past, on Monday at the end of a four-game roadtrip that dropped Phoenix into a tie for the fourth-worst record in the NBA. The Suns are on pace for the worst season in franchise history.
Nash and Sarver work closely with the Spanish Segunda Division soccer team RCD Mallorca. Sarver purchased the team in January and Nash serves on the team's board of directors with final say on personnel matters.
The Suns could discuss the opening with Nash into the offseason. Former Suns coach Mike D'Antoni is also thought to be on Sarver's list.
By Tuesday, the plan is to have an interim head coach in place. Assistant coaches Corey Gaines, Earl Watson and Nate Bjorkgren were scheduled to interview with general manager Ryan McDonough on Monday.
The Suns were 2-15 in January after two of Hornacek's assistants were fired on Dec. 28.
Nash is also heavily involved in Canada's men's basketball Olympic team, which is pegged as a medal challenger in the Summer Olympics in Rio in August.