Yankees manager Joe Girardi said the reliever is scheduled to see a doctor Friday and the team hopes he will be given the go-ahead.
Chapman has not pitched since May 12 because of what Girardi has called tendinitis and bursitis in his left shoulder.
Dellin Betances has closed in Chapman's absence, with Tyler Clippard moved back to the eighth inning and Adam Warren to the seventh. Warren wasted a seventh-inning lead in Tuesday's 6-2 loss to Kansas City, the second blown lead in five games for New York's bullpen.
Chad Green has been used in long relief.
"The loss of Chapman has really changed Adam's role the most," Girardi said. "In having Chad Green, you have to be somewhat careful because he's a starter. He's not a guy that's used to going back to back. We try to pitch him multiple innings but in doing that we have to give him a couple days off.
Masahiro Tanaka has not been sent for scans. New York's ace starter has allowed 14 runs and seven homers over 4 2/3 innings in his last two starts, raising his ERA to 6.56. He is scheduled to start Thursday's series finale.
"We don't want to turn him into Spider-Man or Superman or something like that. Radiation is something you have to deal with, so, no, you just don't scan people to scan them," Girardi said. "We have to do that at the airport, and none of us like that."
First baseman Greg Bird, who hasn't played since May 1 because of a bone bruise in his right ankle, is slated to head to Tampa, Florida, on Sunday, play one game at extended spring training and then start an injury rehabilitation assignment with Class A Tampa.