Chapman is scheduled to pitch one inning for Class A Dayton on Thursday and will make at least four rehab appearances.
Chapman suffered multiple fractures above his left eye and nose and a concussion after being struck by a ball hit by Kansas City Royals catcher Salvador Perez in a spring training game on March 19.
He threw 25 pitches during batting practice on Tuesday and took pitchers fielding practice for the first time since being injured.
"We anticipate a minimum of four outings with the necessary spacing between those outings, so we're looking at another seven-to-10 days, I'd guess," Price said, via the Cincinnati Enquirer.JAFFE: Mike Trout, Justin Upton, Johnny Cueto lead April’s group of All-Stars
"We have a schedule, we have a template, we're not going through this blindly, but with that said we'd like to have the freedom of allowing him to see how he feels after he throws in these games and not have this teaser for everybody," Price said.