Until Venters returns, however, manager Fredi Gonzalez is willing to use right-hander Jordan Walden in relief against left-handed hitters.
"Having Walden get left-handers out almost better than he does right-handers, that's almost like your second lefty," Gonzalez said. "We did that a little bit last year."
Walden held left-handed hitters to a .190 batting average in 91 plate appearances in 2013, his first season with the Braves. Right-handers batted .247 against Walden, who recorded a 3.47 ERA in 50 appearances.
Gonzalez also mentioned southpaw Ryan Buchter as a possible fit.
Buchter, 27, has bounced around the Minor Leagues for eight seasons with the Atlanta and Washington organizations. He finished 4-0 with a 2.76 ERA in 51 appearances for Triple-A Gwinnett last season, lowering his career ERA to 3.47 in 366 innings.
Non-roster invitee Atahualpa Severino is another name Gonzalez brought up as a possibility to fill the role. Severino, 29, pitched briefly for the Nationals in 2011, recording a victory and a 3.86 ERA in six appearances.
"[Severino] supposedly throws the ball really well," Gonzalez said.
Meanwhile, Venters continues to improve, and he played catch with infielder Ramiro Pena during Friday's full-squad workout.
"Talking to [head athletic trainer Jeff Porter], he was really, really pleased with how [Venters is] coming along," Gonzalez said.
With Venters dealing with injury since 2012, Avilan has emerged as a formidable left-hander out of the bullpen. Avilan, 24, has compiled a 6-0 record and a 1.69 ERA in 106 appearances for the Braves since 2012.
Left-handed batters have hit only .156 against Avilan during his two-year career.
Joe Morgan is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.