Kehl last played for the club on April 15 and has been struggling with a groin problem since then.
Kirch, meanwhile, played and scored in the 2-2 draw at Bayer Leverkusen on April 26 but has been suffering with a virus and did not feature in the game against Hoffenheim last time out.
On Thursday, coach Jurgen Klopp confirmed that both had resumed training, although caution was being taken with Kehl.
"That was a nasty infection, but Oli goes well again," he said.
It remains to be seen whether either man will feature in Dortmund's last Bundesliga encounter of the season, away at Hertha Berlin on Saturday, with a DFB-Pokal final date with Bayern Munich on May 17 also looming.
Klopp also urged caution about Sven Bender, out since late February with an inflammation of the pubic joint.
"We are putting him and ourselves under no pressure," he said. "One must not take any chances there."
