The Heat could try to draft the point guard to convince LeBron to stay.
ESPN's Chad Ford reports that Miami are aggressively looking to move up in the NBA Draft, which takes place on Thursday, in order to select Napier.
Both James and Heat president Pat Riley are thought to be big fans of the 22-year-old after his impressive play in UConn's run to win the NCAA title last season.
During the championship game, James tweeted: "No way u take a PG in the lottery before Napier."
Now that James has opted out of his contract, the Heat will have to pull out all the stops to keep the four-time MVP on the team. Part one of that plan seems to be to draft Napier, but they will have to trade up to get him.
His stock has risen steadily over the past month, and could even be selected in the lottery come Thursday.
For LeBron though, all that matters at this stage is to win as many championships as possible. He may believe that Napier will be an excellent player in the future, but it is unlikely that a rookie point guard will be enough to convince James that they are ready to win another title next season.
Drafting Napier would be a good first step for the Heat to take in their plan to re-sign LeBron, providing they don't give up too much to get him. However, their ability to retain the superstar power-forward will rest upon how they surround him with veteran players who can help the Heat sooner rather than later.