New general manager Frank Wren spoke with the two-time Cy Young Award winner and his agent, Gregg Clifton.
Wren said Wednesday he will call again next week, after teams can start making offers to free agents.
Glavine spent his first 16 major league seasons with Atlanta, then pitched for the New York Mets for five years. He lives in suburban Atlanta and was hoping to get an offer from the Braves after the 2006 season. Atlanta never made an offer, and he agreed to re-sign with the Mets.
"It wasn't that we weren't interested. It was just the timing of when Tom had to make a decision and when we could make a decision based on our roster and our payroll and where we were at the time," Wren said. "We have flexibility this year to be more active in both the trade market and the free-agent market."
Glavine, a left-hander who turns 42 in March, was 13-8 with a 4.45 ERA for the Mets this year, when he earned his 300th win. He was hit hard in his final two starts as the Mets collapsed down the stretch, including the season- ending loss to Florida when he failed to get out of the first inning.
Clifton said Glavine could make a decision during the week before the winter meetings, which start Dec. 3.