Glavine, 42, met with Braves general manager Frank Wren last week in what was to be a first step toward the pitcher returning to the Braves.
Glavine was offered under $2 million, MLB.com and the Atlanta Journal-Constitution reported. The MLB.com report said it was at least $1 million.
Glavine, who underwent elbow and shoulder surgery in August, received a positive report in a recent visit to Dr. James Andrews in Birmingham, Ala., and was expected to be ready in time for Opening Day.
If Glavine returns to the Braves and is healthy in spring training, he would be the front-runner for the No. 5 spot behind Derek Lowe, Kenshin Kawakami, Javier Vazquez and Jair Jurrjens.
Glavine, a career 305-203 with Atlanta and the New York Mets, posted a 2-4 record with a 5.54 ERA in 13 starts for the Braves last season.
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