In fact, it appears the Braves and Jones have become more disinterested in each other.
When the Dodgers allowed Jones to become a free agent earlier this month, there was an immediate assumption that he would return to the Braves.
But that assumption wasn't shared by Atlanta, which immediately indicated that it likely wouldn't offer the former All-Star outfielder anything more than a Minor League contract.
Agent Scott Boras has said Jones has no interest in entertaining a Minor League deal, and the 31-year-old outfielder seemingly verified this earlier this week, when he became defensive when a former Braves teammate simply suggested that this was an option that would allow him the opportunity to resuscitate his career in the familiar surroundings of Atlanta.
Jones is already guaranteed to make approximately $5 million this year from the Dodgers, who will also pay him nearly $16 million -- the remainder of his 2009 salary -- over the next six years.
Still, Jones is looking for the financial guarantee and roster stability that a Major League contract would bring.
With approximately $6 million to $7 million to spend, Atlanta is in search of an outfielder, and the fact that it still hasn't shown much desire to provide Jones even a small portion of these funds further highlights the concerns it has about bringing him back.
Even if the Braves were to simply offer Jones the Major League minimum salary of $400,000, they would need to create a spot for him on their 40-man roster, and they don't have any interest in doing this to accommodate a player who has hit .205 with a .665 OPS (on-base percentage plus slugging percentage) over the past two seasons.
But the concerns the Braves have about reuniting with Jones extend beyond the possibility of losing a prospect whom they would have to remove from their 40-man roster.
Having signed, developed and employed Jones for the first 12 seasons of his Major League career, the Braves have more of a personal interest in the outfielder than any other club.
But at the same time, knowing him better than any other club has led them to worry about his willingness to make the necessary adjustments to prevent repeating his struggles of this past season, when he hit .158 with three homers in 75 games for the Dodgers.
The pull-happy Jones' stubbornness was never more evident than in early May 2007, when after recording clutch opposite-field hits on consecutive nights, he said, "I'm not a right-field-ball hitter."
With this in mind, Braves players who have been taking batting practice with Jones over the past month haven't allowed themselves to believe his approach and swings are necessarily the same one that he'd display during games.
During Jones' previous tenure in Atlanta, he hit a number of batting-practice pitches over the right-field wall with a ferocity that Chipper Jones said "would make you think they were coming off the bat of a left-handed power hitter."
But when the games began, the veteran outfielder too often let his swing proclaim, "I'm not a right-field-ball hitter."
Providing the benefit of the doubt, some of Jones' struggles in Los Angeles could be blamed on a bothersome right knee that was surgically repaired this past summer. But this doesn't erase the fact that his fall from stardom began two years earlier.
In a 248-game stretch from the beginning of his memorable 2005 season through the first half of the '06 campaign, Jones hit .266 with 71 homers, a .548 slugging percentage and an .895 OPS.
But in the 222-game stretch that followed through the end of the 2007 season, Jones hit just .230 with 47 homers, a .460 slugging percentage and a .793 OPS. This skid prompted the Braves to not even attempt to negotiate a new contract with him when he became a free agent.
In their search to find an outfielder, the Braves are looking at free agents Bobby Abreu and Adam Dunn, as well as potentially trading for Yankees players Nick Swisher and Xavier Nady.
While each of these outfielders would come at a greater cost than Jones, the Braves also view them as better options.
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.