Green was tended to on the sideline before walking to a cart during the team's first day of training camp Saturday in Dayton, Ohio. He was later spotted walking with crutches and with his ankle wrapped up.
"I think we'll let him get checked out," Taylor told reporters. "I don't think anything that's happened today is anything that ... You don't want to assume anything, but I think we're going to be OK."
Green sustained a right toe injury in 2018, forcing him to miss seven games last season. The seven-time Pro Bowl selection finished his last campaign with a career-low 46 catches for 694 yards and six touchdowns. Green had 75 catches for 1,078 yards and eight scores in 16 starts in 2017.
"You never want to see anybody leave, especially when it's your best player is the one going out. I know A.J. is a fast healer," Bengals quarterback Andy Dalton said.
The eight-year veteran is entering the final year of his contract. Green has an $11.9 million base salary in 2019. He recently ranked at No. 58 in the NFL 100, a list of the league's best players voted on by fellow players.