Since reporting to Spring Training, Chapman has thrown in four bullpen sessions and twice faced hitters in live batting practice. He has impressed each time out and demonstrated command of all three of his pitches.
On Monday, Chapman threw around 25-30 pitches in the bullpen with no issues.
"I think his progress is tremendous," said Fossas, who is the Class A Dayton pitching coach and Chapman's confidant. "His mechanics are getting better and he's finishing pitches better. All you guys can see he's around the plate almost every pitch."
Also scheduled to pitch on Thursday are Aaron Harang, Homer Bailey, Enerio Del Rosario, Jordan Smith, Logan Ondrusek, Alexander Smit, Philippe Valiquette and Pedro Viola.
Chapman, who turned 22 on Sunday, has been the focal point of many around the game since he signed a six-year, $30.25 million contract with the Reds in January. He is a defector from Cuba who has thrown a fastball over 100 mph.
Team officials have not ruled out the notion that Chapman could be their rotation's fifth starter out of camp. He is competing against several other contenders, including Micah Owings, Justin Lehr and Matt Maloney.
After all of the bullpen side sessions and batting practice, however, all talks of a big league callup are on hold until the club sees how he fares in real game scenarios. There is no word on when Chapman might make his Cactus League debut.
In the meantime, he is trying to make himself Major League ready.
"In all aspects, I'm just trying to get better every day," Chapman said.
Mark Sheldon is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.