In the Akron Beacon Journal, Brian Windhorst spells it out: Cleveland wanted Michael Finley to go to Miami, not San Antonio, because it would have increased their chances of landing guard Damon Jones.
The Heat now still have all of their $5 million mid-level exception to use, which means they can match or beat the Cavaliers' offer to Jones. More importantly, though, they have a need for another shooter, and Jones is the best on the market and wants to return.
While the Cavaliers were waiting on Jones, they had guards Jannero Pargo, Steve Blake and Earl Watson in for free-agent visits. It is likely the team will attempt to sign one of them, if Jones indeed decides to return to the Heat. None of them, however, had been full-time starters in the NBA.