Coppolella addressed Teheran's future with the Braves during an open Q&A session with fans conducted Friday over the team's Twitter account.
In another tweet, Coppolella elaborated on Teheran's value to the Braves, saying the star pitcher is "almost into 'right-arm' type status for us now."
Teheran is expected to attract widespread interest as baseball's Aug. 1 non-waiver trade deadline approaches. Multiple sources told ESPN's Jim Bowden that the Boston Red Sox recently contacted the Braves to inquire about Teheran and young closer Arodys Vizcaino, although there was no traction to the talks.
Coppolella previously told Fox Sports that the Braves would have to be overwhelmed by a trade offer in order to part with Teheran, who is in his sixth year in the majors and has spent his entire professional career with the Braves.
Teheran, 25, is 3-7 with a 2.66 ERA -- the 10th-best mark in the National League -- in 15 starts this season. The right-hander is in the third year of a six-year, $32.4 million deal with the Braves.