Glavine said Friday he believes he was released for financial reasons and to clear a roster spot for Tommy Hanson, who made his major league debut Sunday against the Milwaukee Brewers.
Wren, team chairman Terry McGuirk and president John Schuerholz said Glavine was released because they did not believe the 43-year-old left-hander would make a successful return from surgery on his elbow and shoulder.
"It was purely and only on the merits of what gave us the best chance to win, no financial interest whatsoever involved," McGuirk said.
FoxSports.com reported Saturday that Glavine's agent, Gregg Clifton, is exploring filing a grievance.
Glavine would have received a $1 million bonus if he had been activated from the disabled list for Sunday's start, as he expected.
"I don't believe for a minute that it was totally a performance-related issue, which I'm totally fine with, but I would have appreciated the honesty," Glavine said Friday.
According to the collective-bargaining agreement, players can't be released because of financial reasons.
Schuerholz issued an apology Friday for "the environment and the tone and the manner" of the release.
Schuerholz said he should have better explained the decision to Glavine.
"I, as the president of the club, could have taken more time to explain not only the circumstances around the decision, although we made that decision in unanimous fashion, but to explain to Tommy our high regard for him," Schuerholz said, adding he hopes the organization can maintain "some sort of relationship" with Glavine.
"But I don't feel like I really expressed myself as completely and as fully and to the level that somebody like Tommy deserves," Schuerholz said.
Glavine and Clifton did not respond to requests from The Associated Press for comment about the possible grievance.