Before the Yankees opened a series with the Chicago White Sox, manager Aaron Boone said Green was getting other opinions before making a final decision.
Green was injured during Thursday's loss in Baltimore, and before Friday's rainout, Boone said the strain is a significant one.
This season, Green is 1-1 with a 3.00 ERA in 14 appearances. Since becoming one of New York's high-leverage relievers in 2017, he has a 2.96 ERA in 260 appearances. Last season, Green was 10-7 with a 3.12 ERA in 67 appearances, striking out 99 hitters in 83⅔ innings.
"He's on that very short list of outstanding relievers in our sport," Boone said. "He's been so consistent, such a rock for us. He's just a consistent pitcher, a person. Just so reliable and an important part of our team, that room. So it's definitely tough."
To replace Green, Ron Marinaccio was recalled from Triple-A Scranton/Wilkes Barre for his third stint with the Yankees. In two prior times with the team, he had an 11.25 ERA in four appearances.