Now it appears the Heat have backed off from pursuing Paul entirely.
Kevin O'Connor of The Ringer reported Miami's trade interest in Paul is "extinct," noting the Heat are more likely to pursue a trade for Jrue Holiday.
Paul, 34, is in the midst of a solid first season with the Oklahoma City Thunder. He's averaging 16.2 points, 6.3 assists and 4.5 rebounds while keeping the Thunder—a team essentially built of veteran trade pieces—in playoff contention.
While the Heat would probably love to add Paul as a player, his contract makes a trade prohibitive. He's owed an average of more than $40 million per season over the next three years. Trading him requires matching salaries that would gut Miami of its depth, a significant deterrent given the team's hot start.
Paul is also in the waning moments of his NBA career, a guy who may be playing on his final contract. It's likely he'll remain a good player for the next couple of seasons, but the Heat are in need of a difference-making star—not a solid veteran absorbing $40 million-plus of their cap.
The Thunder are in an awkward position with Paul because he's both too valuable as a player to waive outright but so expensive that few teams have the space or willingness to bring him in. They're more likely to prioritize younger pieces like Holiday, who is both younger and a better player at this point than Paul.
The best potential scenario is some sort of buyout being reached by the Thunder and Paul next summer, whereby he takes a significant pay cut for his freedom. Paul could then look to sign elsewhere and recoup most (if not all) of the money from his bought out contract.