Roma pair in race to be fit for Champions League semi-final second leg
The injuries came in Tuesday's 5-2 humbling by Liverpool at Anfield in the first leg, with Strootman sustaining bruised ribs and Perotti spraining his left ankle.
The duo will both sit out the visit of Chievo in Serie A on Saturday and will be assessed early next week to determine their availability for the second leg at the Stadio Olimpico.
Should they not make it, Roma boss Eusebio Di Francesco's taks of overturning a three-goal deficit for the second round in a row will become even more difficult, but he is refusing to give up hope.
"This tie is still alive," he explained. "We let in four at the Camp Nou and here we let in five - it could have been even more at one stage.
"But hope is still there. We don't need miracles, we just need to believe in what we do against a quality team. Our fans will be behind us, supporting throughout."