Sarr was withdrawn in the first-half of Sunday's 2-1 defeat against Manchester United, replaced by fellow forward Eddie Nketiah after first receiving treatment during the opening minutes.
But Glasner is optimistic the Senegalese forward will be back in time for the Africa Cup of Nations with his country Senegal. However, he will undergo further assessments before a final decision is made.
The manager also confirmed that Borna Sosa will miss the game at Turf Moor, but is hopeful to have the Croatian back for Sunday's game against Fulham.
Bar those two, Glasner has no fresh injury concerns for the midweek meeting with Burnley.
"Ismaïla Sarr is out for this game," he told his pre-match press conference. "Honestly, it doesn't look too bad, but he will definitely miss both games this week.
"There are some issues with his ankle ligaments. They are not completely torn, but there are some issues with the ankle, very swollen.
"But we are still hopeful, and I know our medical department and how hard they are working.
"We have hope that he could return before AFCON, but we have to do further assessments and of course have to see how the next days are going for him.
"Borna Sosa is again not available, but we hope to have him against Fulham. But all others who were involved in Sunday's game are ready."
Match Details
Burnley v Crystal Palace
- Wednesday, 3rd December
- 19:30 GMT
- Premier League
- Turf Moor
- Live audio commentary on Palace TV+.