The Miami Heat is a ready-built contender. They have a superstar in Jimmy Butler, and they made the Finals in 2020 but fell short of beating LeBron James' Los Angeles Lakers. It would make sense that they would want to upgrade their roster, after coming so close to the NBA championship. The biggest star on the market is James Harden, so that would be the most obvious way to upgrade.
The Miami Heat were actually linked to James Harden, with some saying that a trade could happen before the start of the season on the 22nd. However, Ira Winderman, a Miami Heat reporter stated that their interest may have cooled, and Bleacher Report summarized the situation.
The Miami Heat could have traded James Harden for a chance to overload their roster with star power, creating a big three of Jimmy Butler, Bam Adebayo, and James Harden. That trio would be a menace scoring-wise, and could easily compete with the juggernauts of the Eastern Conference. However, with the Miami Heat pulling out of the conversations, and never really going deep into the trade talks, it looks like their roster is staying put.
For James Harden, the time is rapidly running out to get out of Houston. The Rockets seem comfortable waiting out the bidding war and getting the best offer possible. The Miami Heat seem to be done with the talks for now, so the list of suitors for Harden grows lower. Hopefully, that means the Rockets will be able to pick a package soon and let the trade rumors go to rest.