Both are currently on the 15-day disabled list, and Gagne also left the team during the weekend to be with his wife, who has had complications during her pregnancy.
Brewers manager Ned Yost said Gagne (rotator cuff tendinitis) was expected to rejoin the team on Monday night as the Brewers took on the Arizona Diamondbacks.
Riske (hyperextended elbow) threw catch in the outfield on Monday with the trainer, and Yost said the righty felt good during the session in what's been a longer than expected recovery time since Riske was put on the DL on May 15.
Gagne, who went to the DL retroactive to May 21, has also been playing catch and is eligible to return Thursday, but Yost said neither player is close to being activated, ruling them out from returning to action this week.
"I don't see how that's possible. Riske's just now playing catch where he feels good, and he hasn't been on the mound. And Gagne's been playing catch, too, but he hasn't been on the mound either," Yost said. "We're close, but we're not there."
In the last 10 games, the Brewers' bullpen has settled from its early season woes, allowing just four runs in 28 innings to drop its overall ERA from 4.60 to 4.07.
Salomon Torres is 1-0 and has four saves in his five appearances since taking over in the closer's role in place of Gagne, who signed a one-year, $10 million contract this offseason and is 1-2 with a 6.98 ERA with 10 saves in 15 chances.
Riske, who signed a three-year deal, is 0-1 with a 4.71 ERA in 18 appearances.
"He's playing catch today. Right now, we're not much past that," Yost said. "We're going to take it day by day, but he's feeling much, much better."
Yost said once the two get on the mound, it'll be several more days before they'll be ready to be activated.
"You just need to regain your strength, regain your durability so to speak and get your strength back up so that you can compete for 20, 25 pitches," Yost said. "You don't just throw them back in there."