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MIAMI — The conventional wisdom is that the Miami Heat rebounded reasonably well this offseason from the loss of the game's premier player, re-signing Chris Bosh, Dwyane Wade and Udonis Haslem, adding veterans Luol Deng, Josh McRoberts and Danny Granger and drafting Shabazz Napier to inject some overdue youth along with James Ennis.

But even if they exceed expectations, that won't completely curtail conversation about what could have been, not just if LeBron James had stayed but also about who they could have added to complement him.

In separate conversations with Bleacher Report, which took place Monday in Columbus and Tuesday in Miami, current Chicago Bulls forward/center Pau Gasol and current Houston Rockets forward Trevor Ariza spoke of the Heat's recruiting efforts during the free-agency period and how strongly each considered moving to Miami.

The Heat liked both players—Gasol as a complement to Bosh in the frontcourt and Ariza as a wing defender and three-point shooter to replace the retired Shane Battier.

Clearly, Miami is a city both players like.

Ariza was born there.

And when told that this particular reporter was from there, Gasol smiled, "Miami? Oh, good for you."

After spending six-plus seasons with the Los Angeles Lakers, how close was Gasol to remaining in warm weather and joining the Heat?

"We had a few conversations," Gasol said. "We met in Los Angeles as well. But their situation wasn't clear at the time."

That occurred over the July 4th weekend.

"They couldn't really give me certainty of certain things," Gasol said. "Of LeBron..."

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James, after opting out of his contract, had yet to commit to returning to Miami; later, Pat Riley revealed that James hadn't been returning his texts or emails.

"So that was important, as far as my decision went," Gasol said. "So at the time that I made my decision, basically it still wasn't clear. It seemed like LeBron wasn't going to go back, so I felt like Chicago was going to be a better fit for me."

Gasol agreed to a three-year, $22 million contract with the Bulls on July 12, one day after James' essay in Sports Illustrated announced a return to the Cleveland Cavaliers, although that did come after the Bulls and Lakers had been unsuccessfully attempting to work out a sign-and-trade deal.

Gasol confirmed that Bosh and Wade reached out to recruit him.

"Obviously, I respect them a lot," Gasol said. "I appreciate their interest. And it really would have been nice to play with a lot of guys [who] reached out to me, excellent players, Hall of Famers, a lot of them. But I could only play for one team, and I decided that Chicago was the best way to go for me."

Since James left, there have been reports—including one from ESPN Radio's Dan Le Batard—that James had advised Gasol not to sign in Miami because he would not be around, an accusation that fits with the organization's perception that his mind was made up long before he informed Riley. Sources close to James have disputed that premise generally, as well as the Gasol report specifically.

Did James steer Gasol from the Heat?

"No, that's speculation, that's not accurate," Gasol said. "No. I communicated with LeBron as well, but that was not mentioned. No."

Now Gasol is a core piece on what is expected to be Cleveland's primary competition in the East.

"So far, I'm still trying to figure things out, get into a better rhythm sometimes," Gasol said. "But I think I fit in nicely, I add to the team. And I like our team and our chances...I think it's an improvement from the situation that I was in the last couple of years. And now it's just a question of giving everything you have, every single night, so you get more comfortable and more used to it, with your teammates, and your teammates with [you]."

While James' presence mattered to Gasol, it was less of a concern to Ariza.

"They talked to me the whole time," Ariza said of the Heat, who also met with him in Los Angeles over July 4th weekend. "Nobody really knew what he was going to do. And my decision wasn't going to be based off what he did."

Ariza felt like it would have been a "plus" to play with James or to fill some of his role.

"So it was a win-win for me," Ariza said, laughing.

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Ariza called the free-agent process "humbling" and "crazy," and said that Riley's pitch, about organizational culture, was "great."

"He's really good at it," Ariza said, laughing.

And yes, joining the Heat was tempting to him.

"[Miami] is like home to me," Ariza said, smiling. "And it was very, very tough to have to go a different direction from Mr. Pat Riley. But they showed a lot of interest in me. I'm very grateful for it. But I felt like Houston was the best fit for me."

Ariza said it didn't come down to money, though the Heat, when they thought James was returning, were operating as a capped team and offering free agents the capped-out mid-level exception starting at about $5.4 million per season. Later, when James left, Miami had more money at hand and gave much of that to Luol Deng, at two years and $20 million, to be their new starting small forward.

The Rockets ultimately signed Ariza for four years and $32 million to be their starting small forward, in place of Chandler Parsons, who was allowed to leave for Dallas as a restricted free agent.

Ethan Skolnick covers the NBA for Bleacher Report. Follow him on Twitter, @EthanJSkolnick.