"I'm not coming back to the Suns if there isn't improvement," Nash told "The Dan Patrick Show".
Nash explained he's expecting the Suns to try to make those improvements, but that he's looking forward to becoming a free agent and deciding where to continue his career.
The hypothetical of LeBron James asking Nash to join up in Miami for one last push at a championship was brought up.
"I would listen," Nash said. "He's phenomenal. I love what they're doing there. A lot of people don't like them because they put all that talent there. But they're professional, they play hard, they play together. Their coaching staff has done a great job, so I have a tremendous amount of respect for them.
"I would definitely listen."
It shouldn't surprise anyone the 38-year-old point guard without a world championship might be enticed by the idea of joining a contender that has what many consider a relative hole at the point guard slot.
Keeping the Heat in the conversation could be used as leverage in negotiations with other teams. But joining the Heat would mean that Nash would be leaving millions of dollars on the table.
The Heat won't have any salary-cap space next summer, so Nash would have to settle for the mid-level exception if he wanted to join the club.
Plenty of teams, including the Suns, could offer much more money than the Heat.
But for someone who has earned about $120 million during his career, sacrificing some money for winning a title might be palatable to Nash.
The 38-year-old Nash is averaging 12 points and 11 assists with a true shooting percentage (which incorporates 2-point shots, 3-point shots and free throw percentage together) of 62.7.