Smoltz, the only pitcher in baseball history with at least 200 wins and 150 saves, has a severely inflamed biceps tendon and inflammation of the rotator cuff of his right shoulder.
There is no immediate timetable for Smoltz to return to the 25-man roster. The 40-year-old right-hander is 3-2 with a 2.00 ERA in five starts this year.
"It would be great if he could be out there and be part of that bullpen," Cox said. "It may be easier on that shoulder. I can visualize him locking up a lot of games for us."
Smoltz returned to the rotation before the start of the 2005 season. He averaged 33 starts over the next three years, going a combined 44-24 with a 3.32 ERA.
Smoltz became the 16th pitcher with 3,000 career strikeouts on April 22. He hopes to have a better idea about his future over the couple of weeks, but the 1996 NL Cy Young Award winner didn't sound as if he will return to the rotation.
Smoltz believes his best-case scenario to pitch in 2008 will be as Atlanta's closer.
"I know I can do the role," he said. "It has everything to do with how my body reacts. The best avenue to come back is to slowly come back. It does me no good to come back to just pitch five innings."
Mike Gonzalez, who had 24 saves for Pittsburgh in 2006, is another option, but the left-hander is still recovering from elbow ligament replacement surgery last year. Gonzalez will leave May 14 for extended spring training before the Braves give him a rehab assignment in the minors.
Smoltz is in the final year of his contract, which pays $14 million this season. He can exercise an option in the deal for $12 million next year if he reaches 200 innings in '08.
That scenario, however, appears unlikely.
"That's just not going to happen, and probably wouldn't if I was still starting," Smoltz said. "There's no reason to fight it, complain or pout. I will just attack the problem. I see it like a puzzle and I just find different pieces. I'm fired up about the challenge. It may not work, but I'm fired up about it."
Smoltz led the NL with 55 saves in 2002, his first full season as closer.